diff --git a/model/histogram/histogram.go b/model/histogram/histogram.go
index 5a2ddea340..42ce8eb99d 100644
--- a/model/histogram/histogram.go
+++ b/model/histogram/histogram.go
@@ -14,7 +14,9 @@
 package histogram
 
 import (
+	"fmt"
 	"math"
+	"strings"
 )
 
 // Histogram encodes a sparse, high-resolution histogram. See the design
@@ -65,7 +67,7 @@ type Span struct {
 }
 
 // Copy returns a deep copy of the Histogram.
-func (h Histogram) Copy() Histogram {
+func (h Histogram) Copy() *Histogram {
 	c := h
 
 	if h.PositiveSpans != nil {
@@ -85,7 +87,61 @@ func (h Histogram) Copy() Histogram {
 		copy(c.NegativeBuckets, h.NegativeBuckets)
 	}
 
-	return c
+	return &c
+}
+
+// String returns a string representation of the Histogram.
+func (h Histogram) String() string {
+	var sb strings.Builder
+	fmt.Fprintf(&sb, "{count:%d, sum:%g", h.Count, h.Sum)
+
+	var nBuckets []Bucket
+	for it := h.NegativeBucketIterator(); it.Next(); {
+		bucket := it.At()
+		if bucket.Count != 0 {
+			nBuckets = append(nBuckets, it.At())
+		}
+	}
+	for i := len(nBuckets) - 1; i >= 0; i-- {
+		fmt.Fprintf(&sb, ", %s", nBuckets[i].String())
+	}
+
+	if h.ZeroCount != 0 {
+		fmt.Fprintf(&sb, ", %s", h.ZeroBucket().String())
+	}
+
+	for it := h.PositiveBucketIterator(); it.Next(); {
+		bucket := it.At()
+		if bucket.Count != 0 {
+			fmt.Fprintf(&sb, ", %s", bucket.String())
+		}
+	}
+
+	sb.WriteRune('}')
+	return sb.String()
+}
+
+// ZeroBucket returns the zero bucket.
+func (h Histogram) ZeroBucket() Bucket {
+	return Bucket{
+		Lower:          -h.ZeroThreshold,
+		Upper:          h.ZeroThreshold,
+		LowerInclusive: true,
+		UpperInclusive: true,
+		Count:          h.ZeroCount,
+	}
+}
+
+// PositiveBucketIterator returns a BucketIterator to iterate over all positive
+// buckets in ascending order (starting next to the zero bucket and going up).
+func (h Histogram) PositiveBucketIterator() BucketIterator {
+	return newRegularBucketIterator(&h, true)
+}
+
+// NegativeBucketIterator returns a BucketIterator to iterate over all negative
+// buckets in descending order (starting next to the zero bucket and going down).
+func (h Histogram) NegativeBucketIterator() BucketIterator {
+	return newRegularBucketIterator(&h, false)
 }
 
 // CumulativeBucketIterator returns a BucketIterator to iterate over a
@@ -96,7 +152,7 @@ func (h Histogram) CumulativeBucketIterator() BucketIterator {
 	if len(h.NegativeBuckets) > 0 {
 		panic("CumulativeIterator called on Histogram with negative buckets")
 	}
-	return &cumulativeBucketIterator{h: h, posSpansIdx: -1}
+	return &cumulativeBucketIterator{h: &h, posSpansIdx: -1}
 }
 
 // BucketIterator iterates over the buckets of a Histogram, returning decoded
@@ -106,26 +162,126 @@ type BucketIterator interface {
 	Next() bool
 	// At returns the current bucket.
 	At() Bucket
-	// Err returns the current error. It should be used only after iterator is
-	// exhausted, that is `Next` or `Seek` returns false.
-	Err() error
 }
 
-// Bucket represents a bucket (currently only a cumulative one with an upper
-// inclusive bound and a cumulative count).
+// Bucket represents a bucket with lower and upper limit and the count of
+// samples in the bucket. It also specifies if each limit is inclusive or
+// not. (Mathematically, inclusive limits create a closed interval, and
+// non-inclusive limits an open interval.)
+//
+// To represent cumulative buckets, Lower is set to -Inf, and the Count is then
+// cumulative (including the counts of all buckets for smaller values).
 type Bucket struct {
-	Upper float64
-	Count uint64
+	Lower, Upper                   float64
+	LowerInclusive, UpperInclusive bool
+	Count                          uint64
+	Index                          int32 // Index within schema. To easily compare buckets that share the same schema.
+}
+
+// String returns a string representation, using the usual mathematical notation
+// of '['/']' for inclusive bounds and '('/')' for non-inclusive bounds.
+func (b Bucket) String() string {
+	var sb strings.Builder
+	if b.LowerInclusive {
+		sb.WriteRune('[')
+	} else {
+		sb.WriteRune('(')
+	}
+	fmt.Fprintf(&sb, "%g,%g", b.Lower, b.Upper)
+	if b.UpperInclusive {
+		sb.WriteRune(']')
+	} else {
+		sb.WriteRune(')')
+	}
+	fmt.Fprintf(&sb, ":%d", b.Count)
+	return sb.String()
+}
+
+type regularBucketIterator struct {
+	schema  int32
+	spans   []Span
+	buckets []int64
+
+	positive bool // Whether this is for positive buckets.
+
+	spansIdx   int    // Current span within spans slice.
+	idxInSpan  uint32 // Index in the current span. 0 <= idxInSpan < span.Length.
+	bucketsIdx int    // Current bucket within buckets slice.
+
+	currCount            int64   // Count in the current bucket.
+	currIdx              int32   // The actual bucket index.
+	currLower, currUpper float64 // Limits of the current bucket.
+
+}
+
+func newRegularBucketIterator(h *Histogram, positive bool) *regularBucketIterator {
+	r := &regularBucketIterator{schema: h.Schema, positive: positive}
+	if positive {
+		r.spans = h.PositiveSpans
+		r.buckets = h.PositiveBuckets
+	} else {
+		r.spans = h.NegativeSpans
+		r.buckets = h.NegativeBuckets
+	}
+	return r
+}
+
+func (r *regularBucketIterator) Next() bool {
+	if r.spansIdx >= len(r.spans) {
+		return false
+	}
+	span := r.spans[r.spansIdx]
+	// Seed currIdx for the first bucket.
+	if r.bucketsIdx == 0 {
+		r.currIdx = span.Offset
+	} else {
+		r.currIdx++
+	}
+	for r.idxInSpan >= span.Length {
+		// We have exhausted the current span and have to find a new
+		// one. We'll even handle pathologic spans of length 0.
+		r.idxInSpan = 0
+		r.spansIdx++
+		if r.spansIdx >= len(r.spans) {
+			return false
+		}
+		span = r.spans[r.spansIdx]
+		r.currIdx += span.Offset
+	}
+
+	r.currCount += r.buckets[r.bucketsIdx]
+	if r.positive {
+		r.currUpper = getBound(r.currIdx, r.schema)
+		r.currLower = getBound(r.currIdx-1, r.schema)
+	} else {
+		r.currLower = -getBound(r.currIdx, r.schema)
+		r.currUpper = -getBound(r.currIdx-1, r.schema)
+	}
+
+	r.idxInSpan++
+	r.bucketsIdx++
+	return true
+}
+
+func (r *regularBucketIterator) At() Bucket {
+	return Bucket{
+		Count:          uint64(r.currCount),
+		Lower:          r.currLower,
+		Upper:          r.currUpper,
+		LowerInclusive: r.currLower < 0,
+		UpperInclusive: r.currUpper > 0,
+		Index:          r.currIdx,
+	}
 }
 
 type cumulativeBucketIterator struct {
-	h Histogram
+	h *Histogram
 
 	posSpansIdx   int    // Index in h.PositiveSpans we are in. -1 means 0 bucket.
 	posBucketsIdx int    // Index in h.PositiveBuckets.
 	idxInSpan     uint32 // Index in the current span. 0 <= idxInSpan < span.Length.
 
-	initialised         bool
+	initialized         bool
 	currIdx             int32   // The actual bucket index after decoding from spans.
 	currUpper           float64 // The upper boundary of the current bucket.
 	currCount           int64   // Current non-cumulative count for the current bucket. Does not apply for empty bucket.
@@ -158,24 +314,24 @@ func (c *cumulativeBucketIterator) Next() bool {
 
 	if c.emptyBucketCount > 0 {
 		// We are traversing through empty buckets at the moment.
-		c.currUpper = getUpper(c.currIdx, c.h.Schema)
+		c.currUpper = getBound(c.currIdx, c.h.Schema)
 		c.currIdx++
 		c.emptyBucketCount--
 		return true
 	}
 
 	span := c.h.PositiveSpans[c.posSpansIdx]
-	if c.posSpansIdx == 0 && !c.initialised {
+	if c.posSpansIdx == 0 && !c.initialized {
 		// Initialising.
 		c.currIdx = span.Offset
-		// The first bucket is absolute value and not a delta with Zero bucket.
+		// The first bucket is an absolute value and not a delta with Zero bucket.
 		c.currCount = 0
-		c.initialised = true
+		c.initialized = true
 	}
 
 	c.currCount += c.h.PositiveBuckets[c.posBucketsIdx]
 	c.currCumulativeCount += uint64(c.currCount)
-	c.currUpper = getUpper(c.currIdx, c.h.Schema)
+	c.currUpper = getBound(c.currIdx, c.h.Schema)
 
 	c.posBucketsIdx++
 	c.idxInSpan++
@@ -191,15 +347,19 @@ func (c *cumulativeBucketIterator) Next() bool {
 
 	return true
 }
+
 func (c *cumulativeBucketIterator) At() Bucket {
 	return Bucket{
-		Upper: c.currUpper,
-		Count: c.currCumulativeCount,
+		Upper:          c.currUpper,
+		Lower:          math.Inf(-1),
+		UpperInclusive: true,
+		LowerInclusive: true,
+		Count:          c.currCumulativeCount,
+		Index:          c.currIdx - 1,
 	}
 }
-func (c *cumulativeBucketIterator) Err() error { return nil }
 
-func getUpper(idx, schema int32) float64 {
+func getBound(idx, schema int32) float64 {
 	if schema < 0 {
 		return math.Ldexp(1, int(idx)<<(-schema))
 	}
diff --git a/model/histogram/histogram_test.go b/model/histogram/histogram_test.go
index 2a33fdb85b..8ef9da69bb 100644
--- a/model/histogram/histogram_test.go
+++ b/model/histogram/histogram_test.go
@@ -15,15 +15,72 @@ package histogram
 
 import (
 	"fmt"
+	"math"
 	"testing"
 
 	"github.com/stretchr/testify/require"
 )
 
+func TestHistogramString(t *testing.T) {
+	cases := []struct {
+		histogram      Histogram
+		expectedString string
+	}{
+		{
+			histogram: Histogram{
+				Schema: 0,
+			},
+			expectedString: "{count:0, sum:0}",
+		},
+		{
+			histogram: Histogram{
+				Schema:        0,
+				Count:         9,
+				Sum:           -3.1415,
+				ZeroCount:     12,
+				ZeroThreshold: 0.001,
+				NegativeSpans: []Span{
+					{Offset: 0, Length: 5},
+					{Offset: 1, Length: 1},
+				},
+				NegativeBuckets: []int64{1, 2, -2, 1, -1, 0},
+			},
+			expectedString: "{count:9, sum:-3.1415, [-64,-32):1, [-16,-8):1, [-8,-4):2, [-4,-2):1, [-2,-1):3, [-1,-0.5):1, [-0.001,0.001]:12}",
+		},
+		{
+			histogram: Histogram{
+				Schema: 0,
+				Count:  19,
+				Sum:    2.7,
+				PositiveSpans: []Span{
+					{Offset: 0, Length: 4},
+					{Offset: 0, Length: 0},
+					{Offset: 0, Length: 3},
+				},
+				PositiveBuckets: []int64{1, 2, -2, 1, -1, 0, 0},
+				NegativeSpans: []Span{
+					{Offset: 0, Length: 5},
+					{Offset: 1, Length: 0},
+					{Offset: 0, Length: 1},
+				},
+				NegativeBuckets: []int64{1, 2, -2, 1, -1, 0},
+			},
+			expectedString: "{count:19, sum:2.7, [-64,-32):1, [-16,-8):1, [-8,-4):2, [-4,-2):1, [-2,-1):3, [-1,-0.5):1, (0.5,1]:1, (1,2]:3, (2,4]:1, (4,8]:2, (8,16]:1, (16,32]:1, (32,64]:1}",
+		},
+	}
+
+	for i, c := range cases {
+		t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
+			actualString := c.histogram.String()
+			require.Equal(t, c.expectedString, actualString)
+		})
+	}
+}
+
 func TestCumulativeBucketIterator(t *testing.T) {
 	cases := []struct {
-		histogram                 Histogram
-		expectedCumulativeBuckets []Bucket
+		histogram       Histogram
+		expectedBuckets []Bucket
 	}{
 		{
 			histogram: Histogram{
@@ -34,14 +91,14 @@ func TestCumulativeBucketIterator(t *testing.T) {
 				},
 				PositiveBuckets: []int64{1, 1, -1, 0},
 			},
-			expectedCumulativeBuckets: []Bucket{
-				{Upper: 1, Count: 1},
-				{Upper: 2, Count: 3},
+			expectedBuckets: []Bucket{
+				{Lower: math.Inf(-1), Upper: 1, Count: 1, LowerInclusive: true, UpperInclusive: true, Index: 0},
+				{Lower: math.Inf(-1), Upper: 2, Count: 3, LowerInclusive: true, UpperInclusive: true, Index: 1},
 
-				{Upper: 4, Count: 3},
+				{Lower: math.Inf(-1), Upper: 4, Count: 3, LowerInclusive: true, UpperInclusive: true, Index: 2},
 
-				{Upper: 8, Count: 4},
-				{Upper: 16, Count: 5},
+				{Lower: math.Inf(-1), Upper: 8, Count: 4, LowerInclusive: true, UpperInclusive: true, Index: 3},
+				{Lower: math.Inf(-1), Upper: 16, Count: 5, LowerInclusive: true, UpperInclusive: true, Index: 4},
 			},
 		},
 		{
@@ -53,16 +110,16 @@ func TestCumulativeBucketIterator(t *testing.T) {
 				},
 				PositiveBuckets: []int64{1, 2, -2, 1, -1, 0},
 			},
-			expectedCumulativeBuckets: []Bucket{
-				{Upper: 1, Count: 1},
-				{Upper: 2, Count: 4},
-				{Upper: 4, Count: 5},
-				{Upper: 8, Count: 7},
+			expectedBuckets: []Bucket{
+				{Lower: math.Inf(-1), Upper: 1, Count: 1, LowerInclusive: true, UpperInclusive: true, Index: 0},
+				{Lower: math.Inf(-1), Upper: 2, Count: 4, LowerInclusive: true, UpperInclusive: true, Index: 1},
+				{Lower: math.Inf(-1), Upper: 4, Count: 5, LowerInclusive: true, UpperInclusive: true, Index: 2},
+				{Lower: math.Inf(-1), Upper: 8, Count: 7, LowerInclusive: true, UpperInclusive: true, Index: 3},
 
-				{Upper: 16, Count: 8},
+				{Lower: math.Inf(-1), Upper: 16, Count: 8, LowerInclusive: true, UpperInclusive: true, Index: 4},
 
-				{Upper: 32, Count: 8},
-				{Upper: 64, Count: 9},
+				{Lower: math.Inf(-1), Upper: 32, Count: 8, LowerInclusive: true, UpperInclusive: true, Index: 5},
+				{Lower: math.Inf(-1), Upper: 64, Count: 9, LowerInclusive: true, UpperInclusive: true, Index: 6},
 			},
 		},
 		{
@@ -73,14 +130,14 @@ func TestCumulativeBucketIterator(t *testing.T) {
 				},
 				PositiveBuckets: []int64{1, 2, -2, 1, -1, 0, 0},
 			},
-			expectedCumulativeBuckets: []Bucket{
-				{Upper: 1, Count: 1},
-				{Upper: 2, Count: 4},
-				{Upper: 4, Count: 5},
-				{Upper: 8, Count: 7},
-				{Upper: 16, Count: 8},
-				{Upper: 32, Count: 9},
-				{Upper: 64, Count: 10},
+			expectedBuckets: []Bucket{
+				{Lower: math.Inf(-1), Upper: 1, Count: 1, LowerInclusive: true, UpperInclusive: true, Index: 0},
+				{Lower: math.Inf(-1), Upper: 2, Count: 4, LowerInclusive: true, UpperInclusive: true, Index: 1},
+				{Lower: math.Inf(-1), Upper: 4, Count: 5, LowerInclusive: true, UpperInclusive: true, Index: 2},
+				{Lower: math.Inf(-1), Upper: 8, Count: 7, LowerInclusive: true, UpperInclusive: true, Index: 3},
+				{Lower: math.Inf(-1), Upper: 16, Count: 8, LowerInclusive: true, UpperInclusive: true, Index: 4},
+				{Lower: math.Inf(-1), Upper: 32, Count: 9, LowerInclusive: true, UpperInclusive: true, Index: 5},
+				{Lower: math.Inf(-1), Upper: 64, Count: 10, LowerInclusive: true, UpperInclusive: true, Index: 6},
 			},
 		},
 		{
@@ -93,22 +150,22 @@ func TestCumulativeBucketIterator(t *testing.T) {
 				},
 				PositiveBuckets: []int64{1, 2, -2, 1, -1, 0, 3},
 			},
-			expectedCumulativeBuckets: []Bucket{
-				{Upper: 0.6484197773255048, Count: 1}, // -5
-				{Upper: 0.7071067811865475, Count: 4}, // -4
+			expectedBuckets: []Bucket{
+				{Lower: math.Inf(-1), Upper: 0.6484197773255048, Count: 1, LowerInclusive: true, UpperInclusive: true, Index: -5},
+				{Lower: math.Inf(-1), Upper: 0.7071067811865475, Count: 4, LowerInclusive: true, UpperInclusive: true, Index: -4},
 
-				{Upper: 0.7711054127039704, Count: 4}, // -3
-				{Upper: 0.8408964152537144, Count: 4}, // -2
+				{Lower: math.Inf(-1), Upper: 0.7711054127039704, Count: 4, LowerInclusive: true, UpperInclusive: true, Index: -3},
+				{Lower: math.Inf(-1), Upper: 0.8408964152537144, Count: 4, LowerInclusive: true, UpperInclusive: true, Index: -2},
 
-				{Upper: 0.9170040432046711, Count: 5}, // -1
-				{Upper: 1, Count: 7},                  // 1
-				{Upper: 1.0905077326652577, Count: 8}, // 0
+				{Lower: math.Inf(-1), Upper: 0.9170040432046711, Count: 5, LowerInclusive: true, UpperInclusive: true, Index: -1},
+				{Lower: math.Inf(-1), Upper: 1, Count: 7, LowerInclusive: true, UpperInclusive: true, Index: 0},
+				{Lower: math.Inf(-1), Upper: 1.0905077326652577, Count: 8, LowerInclusive: true, UpperInclusive: true, Index: 1},
 
-				{Upper: 1.189207115002721, Count: 8},  // 1
-				{Upper: 1.2968395546510096, Count: 8}, // 2
+				{Lower: math.Inf(-1), Upper: 1.189207115002721, Count: 8, LowerInclusive: true, UpperInclusive: true, Index: 2},
+				{Lower: math.Inf(-1), Upper: 1.2968395546510096, Count: 8, LowerInclusive: true, UpperInclusive: true, Index: 3},
 
-				{Upper: 1.414213562373095, Count: 9},   // 3
-				{Upper: 1.5422108254079407, Count: 13}, // 4
+				{Lower: math.Inf(-1), Upper: 1.414213562373095, Count: 9, LowerInclusive: true, UpperInclusive: true, Index: 4},
+				{Lower: math.Inf(-1), Upper: 1.5422108254079407, Count: 13, LowerInclusive: true, UpperInclusive: true, Index: 5},
 			},
 		},
 		{
@@ -120,17 +177,17 @@ func TestCumulativeBucketIterator(t *testing.T) {
 				},
 				PositiveBuckets: []int64{1, 2, -2, 1, -1, 0},
 			},
-			expectedCumulativeBuckets: []Bucket{
-				{Upper: 0.00390625, Count: 1}, // -2
-				{Upper: 0.0625, Count: 4},     // -1
-				{Upper: 1, Count: 5},          // 0
-				{Upper: 16, Count: 7},         // 1
+			expectedBuckets: []Bucket{
+				{Lower: math.Inf(-1), Upper: 0.00390625, Count: 1, LowerInclusive: true, UpperInclusive: true, Index: -2},
+				{Lower: math.Inf(-1), Upper: 0.0625, Count: 4, LowerInclusive: true, UpperInclusive: true, Index: -1},
+				{Lower: math.Inf(-1), Upper: 1, Count: 5, LowerInclusive: true, UpperInclusive: true, Index: 0},
+				{Lower: math.Inf(-1), Upper: 16, Count: 7, LowerInclusive: true, UpperInclusive: true, Index: 1},
 
-				{Upper: 256, Count: 7},  // 2
-				{Upper: 4096, Count: 7}, // 3
+				{Lower: math.Inf(-1), Upper: 256, Count: 7, LowerInclusive: true, UpperInclusive: true, Index: 2},
+				{Lower: math.Inf(-1), Upper: 4096, Count: 7, LowerInclusive: true, UpperInclusive: true, Index: 3},
 
-				{Upper: 65536, Count: 8},   // 4
-				{Upper: 1048576, Count: 9}, // 5
+				{Lower: math.Inf(-1), Upper: 65536, Count: 8, LowerInclusive: true, UpperInclusive: true, Index: 4},
+				{Lower: math.Inf(-1), Upper: 1048576, Count: 9, LowerInclusive: true, UpperInclusive: true, Index: 5},
 			},
 		},
 		{
@@ -141,12 +198,12 @@ func TestCumulativeBucketIterator(t *testing.T) {
 				},
 				PositiveBuckets: []int64{1, 2, -2, 1, -1},
 			},
-			expectedCumulativeBuckets: []Bucket{
-				{Upper: 0.0625, Count: 1}, // -2
-				{Upper: 0.25, Count: 4},   // -1
-				{Upper: 1, Count: 5},      // 0
-				{Upper: 4, Count: 7},      // 1
-				{Upper: 16, Count: 8},     // 2
+			expectedBuckets: []Bucket{
+				{Lower: math.Inf(-1), Upper: 0.0625, Count: 1, LowerInclusive: true, UpperInclusive: true, Index: -2},
+				{Lower: math.Inf(-1), Upper: 0.25, Count: 4, LowerInclusive: true, UpperInclusive: true, Index: -1},
+				{Lower: math.Inf(-1), Upper: 1, Count: 5, LowerInclusive: true, UpperInclusive: true, Index: 0},
+				{Lower: math.Inf(-1), Upper: 4, Count: 7, LowerInclusive: true, UpperInclusive: true, Index: 1},
+				{Lower: math.Inf(-1), Upper: 16, Count: 8, LowerInclusive: true, UpperInclusive: true, Index: 2},
 			},
 		},
 	}
@@ -154,12 +211,177 @@ func TestCumulativeBucketIterator(t *testing.T) {
 	for i, c := range cases {
 		t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
 			it := c.histogram.CumulativeBucketIterator()
-			actualBuckets := make([]Bucket, 0, len(c.expectedCumulativeBuckets))
+			actualBuckets := make([]Bucket, 0, len(c.expectedBuckets))
 			for it.Next() {
 				actualBuckets = append(actualBuckets, it.At())
 			}
-			require.NoError(t, it.Err())
-			require.Equal(t, c.expectedCumulativeBuckets, actualBuckets)
+			require.Equal(t, c.expectedBuckets, actualBuckets)
+		})
+	}
+}
+
+func TestRegularBucketIterator(t *testing.T) {
+	cases := []struct {
+		histogram               Histogram
+		expectedPositiveBuckets []Bucket
+		expectedNegativeBuckets []Bucket
+	}{
+		{
+			histogram: Histogram{
+				Schema: 0,
+			},
+			expectedPositiveBuckets: []Bucket{},
+			expectedNegativeBuckets: []Bucket{},
+		},
+		{
+			histogram: Histogram{
+				Schema: 0,
+				PositiveSpans: []Span{
+					{Offset: 0, Length: 2},
+					{Offset: 1, Length: 2},
+				},
+				PositiveBuckets: []int64{1, 1, -1, 0},
+			},
+			expectedPositiveBuckets: []Bucket{
+				{Lower: 0.5, Upper: 1, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 0},
+				{Lower: 1, Upper: 2, Count: 2, LowerInclusive: false, UpperInclusive: true, Index: 1},
+
+				{Lower: 4, Upper: 8, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 3},
+				{Lower: 8, Upper: 16, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 4},
+			},
+			expectedNegativeBuckets: []Bucket{},
+		},
+		{
+			histogram: Histogram{
+				Schema: 0,
+				NegativeSpans: []Span{
+					{Offset: 0, Length: 5},
+					{Offset: 1, Length: 1},
+				},
+				NegativeBuckets: []int64{1, 2, -2, 1, -1, 0},
+			},
+			expectedPositiveBuckets: []Bucket{},
+			expectedNegativeBuckets: []Bucket{
+				{Lower: -1, Upper: -0.5, Count: 1, LowerInclusive: true, UpperInclusive: false, Index: 0},
+				{Lower: -2, Upper: -1, Count: 3, LowerInclusive: true, UpperInclusive: false, Index: 1},
+				{Lower: -4, Upper: -2, Count: 1, LowerInclusive: true, UpperInclusive: false, Index: 2},
+				{Lower: -8, Upper: -4, Count: 2, LowerInclusive: true, UpperInclusive: false, Index: 3},
+				{Lower: -16, Upper: -8, Count: 1, LowerInclusive: true, UpperInclusive: false, Index: 4},
+
+				{Lower: -64, Upper: -32, Count: 1, LowerInclusive: true, UpperInclusive: false, Index: 6},
+			},
+		},
+		{
+			histogram: Histogram{
+				Schema: 0,
+				PositiveSpans: []Span{
+					{Offset: 0, Length: 4},
+					{Offset: 0, Length: 0},
+					{Offset: 0, Length: 3},
+				},
+				PositiveBuckets: []int64{1, 2, -2, 1, -1, 0, 0},
+				NegativeSpans: []Span{
+					{Offset: 0, Length: 5},
+					{Offset: 1, Length: 0},
+					{Offset: 0, Length: 1},
+				},
+				NegativeBuckets: []int64{1, 2, -2, 1, -1, 0},
+			},
+			expectedPositiveBuckets: []Bucket{
+				{Lower: 0.5, Upper: 1, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 0},
+				{Lower: 1, Upper: 2, Count: 3, LowerInclusive: false, UpperInclusive: true, Index: 1},
+				{Lower: 2, Upper: 4, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 2},
+				{Lower: 4, Upper: 8, Count: 2, LowerInclusive: false, UpperInclusive: true, Index: 3},
+				{Lower: 8, Upper: 16, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 4},
+				{Lower: 16, Upper: 32, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 5},
+				{Lower: 32, Upper: 64, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 6},
+			},
+			expectedNegativeBuckets: []Bucket{
+				{Lower: -1, Upper: -0.5, Count: 1, LowerInclusive: true, UpperInclusive: false, Index: 0},
+				{Lower: -2, Upper: -1, Count: 3, LowerInclusive: true, UpperInclusive: false, Index: 1},
+				{Lower: -4, Upper: -2, Count: 1, LowerInclusive: true, UpperInclusive: false, Index: 2},
+				{Lower: -8, Upper: -4, Count: 2, LowerInclusive: true, UpperInclusive: false, Index: 3},
+				{Lower: -16, Upper: -8, Count: 1, LowerInclusive: true, UpperInclusive: false, Index: 4},
+
+				{Lower: -64, Upper: -32, Count: 1, LowerInclusive: true, UpperInclusive: false, Index: 6},
+			},
+		},
+		{
+			histogram: Histogram{
+				Schema: 3,
+				PositiveSpans: []Span{
+					{Offset: -5, Length: 2}, // -5 -4
+					{Offset: 2, Length: 3},  // -1 0 1
+					{Offset: 2, Length: 2},  // 4 5
+				},
+				PositiveBuckets: []int64{1, 2, -2, 1, -1, 0, 3},
+			},
+			expectedPositiveBuckets: []Bucket{
+				{Lower: 0.5946035575013605, Upper: 0.6484197773255048, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: -5},
+				{Lower: 0.6484197773255048, Upper: 0.7071067811865475, Count: 3, LowerInclusive: false, UpperInclusive: true, Index: -4},
+
+				{Lower: 0.8408964152537144, Upper: 0.9170040432046711, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: -1},
+				{Lower: 0.9170040432046711, Upper: 1, Count: 2, LowerInclusive: false, UpperInclusive: true, Index: 0},
+				{Lower: 1, Upper: 1.0905077326652577, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 1},
+
+				{Lower: 1.2968395546510096, Upper: 1.414213562373095, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 4},
+				{Lower: 1.414213562373095, Upper: 1.5422108254079407, Count: 4, LowerInclusive: false, UpperInclusive: true, Index: 5},
+			},
+			expectedNegativeBuckets: []Bucket{},
+		},
+		{
+			histogram: Histogram{
+				Schema: -2,
+				PositiveSpans: []Span{
+					{Offset: -2, Length: 4}, // -2 -1 0 1
+					{Offset: 2, Length: 2},  // 4 5
+				},
+				PositiveBuckets: []int64{1, 2, -2, 1, -1, 0},
+			},
+			expectedPositiveBuckets: []Bucket{
+				{Lower: 0.000244140625, Upper: 0.00390625, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: -2},
+				{Lower: 0.00390625, Upper: 0.0625, Count: 3, LowerInclusive: false, UpperInclusive: true, Index: -1},
+				{Lower: 0.0625, Upper: 1, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 0},
+				{Lower: 1, Upper: 16, Count: 2, LowerInclusive: false, UpperInclusive: true, Index: 1},
+
+				{Lower: 4096, Upper: 65536, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 4},
+				{Lower: 65536, Upper: 1048576, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 5},
+			},
+			expectedNegativeBuckets: []Bucket{},
+		},
+		{
+			histogram: Histogram{
+				Schema: -1,
+				PositiveSpans: []Span{
+					{Offset: -2, Length: 5}, // -2 -1 0 1 2
+				},
+				PositiveBuckets: []int64{1, 2, -2, 1, -1},
+			},
+			expectedPositiveBuckets: []Bucket{
+				{Lower: 0.015625, Upper: 0.0625, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: -2},
+				{Lower: 0.0625, Upper: 0.25, Count: 3, LowerInclusive: false, UpperInclusive: true, Index: -1},
+				{Lower: 0.25, Upper: 1, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 0},
+				{Lower: 1, Upper: 4, Count: 2, LowerInclusive: false, UpperInclusive: true, Index: 1},
+				{Lower: 4, Upper: 16, Count: 1, LowerInclusive: false, UpperInclusive: true, Index: 2},
+			},
+			expectedNegativeBuckets: []Bucket{},
+		},
+	}
+
+	for i, c := range cases {
+		t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
+			it := c.histogram.PositiveBucketIterator()
+			actualPositiveBuckets := make([]Bucket, 0, len(c.expectedPositiveBuckets))
+			for it.Next() {
+				actualPositiveBuckets = append(actualPositiveBuckets, it.At())
+			}
+			require.Equal(t, c.expectedPositiveBuckets, actualPositiveBuckets)
+			it = c.histogram.NegativeBucketIterator()
+			actualNegativeBuckets := make([]Bucket, 0, len(c.expectedNegativeBuckets))
+			for it.Next() {
+				actualNegativeBuckets = append(actualNegativeBuckets, it.At())
+			}
+			require.Equal(t, c.expectedNegativeBuckets, actualNegativeBuckets)
 		})
 	}
 }
diff --git a/promql/engine_test.go b/promql/engine_test.go
index 88eed7f8bb..941250a415 100644
--- a/promql/engine_test.go
+++ b/promql/engine_test.go
@@ -2460,4 +2460,5 @@ func TestSparseHistogramRate(t *testing.T) {
 	require.NoError(t, err)
 	res := qry.Exec(test.Context())
 	require.NoError(t, res.Err)
+	fmt.Println(res)
 }
diff --git a/tsdb/compact_test.go b/tsdb/compact_test.go
index 5f3d2374b6..b0df493f73 100644
--- a/tsdb/compact_test.go
+++ b/tsdb/compact_test.go
@@ -1533,7 +1533,6 @@ func TestSparseHistogramSpaceSavings(t *testing.T) {
 								require.NoError(t, err)
 								itIdx++
 							}
-							require.NoError(t, it.Err())
 							// _count metric.
 							countLbls := ah.baseLabels.Copy()
 							countLbls[0].Value = countLbls[0].Value + "_count"