diff --git a/include/common/htx.h b/include/common/htx.h
index 78e62a500..003680a2b 100644
--- a/include/common/htx.h
+++ b/include/common/htx.h
@@ -152,8 +152,8 @@ struct htx {
 
 	uint32_t used;   /* number of blocks in use */
 	uint32_t tail;   /* last inserted block */
+	uint32_t head;   /* older inserted block */
 	uint32_t front;  /* block's position of the first content before the blocks table */
-	uint32_t wrap;   /* the position were the blocks table wraps, if any */
 
 	uint64_t extra;  /* known bytes amount remaining to receive */
 	uint32_t flags;  /* HTX_FL_* */
@@ -345,6 +345,21 @@ static inline uint32_t htx_get_blksz(const struct htx_blk *blk)
 	}
 }
 
+/* Returns the wrap position, ie the position where the blocks table wraps.
+ *
+ * An signed 32-bits integer is returned to handle -1 case. Blocks position are
+ * store on unsigned 32-bits integer, but it is impossible to have so much
+ * blocks to overflow a 32-bits signed integer !
+ */
+static inline int32_t htx_get_wrap(const struct htx *htx)
+{
+	if (!htx->used)
+		return -1;
+	return ((htx->tail >= htx->head)
+		? (htx->used + htx->head)
+		: (htx->used - 1) + (htx->head - htx->tail));
+}
+
 /* Returns the position of the oldest entry (head).
  *
  * An signed 32-bits integer is returned to handle -1 case. Blocks position are
@@ -353,10 +368,7 @@ static inline uint32_t htx_get_blksz(const struct htx_blk *blk)
  */
 static inline int32_t htx_get_head(const struct htx *htx)
 {
-	if (!htx->used)
-		return -1;
-
-	return (((htx->tail + 1U < htx->used) ? htx->wrap : 0) + htx->tail + 1U - htx->used);
+	return (htx->used ? htx->head : -1);
 }
 
 /* Returns the oldest HTX block (head) if the HTX message is not
@@ -424,8 +436,10 @@ static inline int32_t htx_get_prev(const struct htx *htx, uint32_t pos)
 	head = htx_get_head(htx);
 	if (head == -1 || pos == head)
 		return -1;
-	if (!pos)
-		return (htx->wrap - 1);
+	if (!pos) {
+		/* htx_get_wrap() is always greater than 1 here */
+		return (htx_get_wrap(htx) - 1);
+	}
 	return (pos - 1);
 }
 
@@ -450,14 +464,11 @@ static inline struct htx_blk *htx_get_prev_blk(const struct htx *htx,
  */
 static inline int32_t htx_get_next(const struct htx *htx, uint32_t pos)
 {
-	if (!htx->used)
-		return -1;
-
-	if (pos == htx->tail)
+	if (!htx->used || pos == htx->tail)
 		return -1;
 	pos++;
-	if (pos >= htx->wrap)
-		pos = 0;
+	if (pos == htx_get_wrap(htx))
+		return 0;
 	return pos;
 
 }
@@ -663,7 +674,7 @@ static inline int htx_almost_full(const struct htx *htx)
 
 static inline void htx_reset(struct htx *htx)
 {
-	htx->data = htx->used = htx->tail = htx->wrap  = htx->front = 0;
+	htx->data = htx->used = htx->tail = htx->head  = htx->front = 0;
 	htx->extra = 0;
 	htx->flags = HTX_FL_NONE;
 	htx->sl_off = -1;
@@ -779,11 +790,10 @@ static inline void htx_dump(struct htx *htx)
 	int32_t pos;
 
 	fprintf(stderr, "htx:%p [ size=%u - data=%u - used=%u - wrap=%s - extra=%llu]\n",
-		htx, htx->size, htx->data, htx->used,
-		(!htx->used || htx->tail+1 == htx->wrap) ? "NO" : "YES",
+		htx, htx->size, htx->data, htx->used, (htx->tail >= htx->head) ? "NO" : "YES",
 		(unsigned long long)htx->extra);
-	fprintf(stderr, "\thead=%d - tail=%u - front=%u - wrap=%u\n",
-		htx_get_head(htx), htx->tail, htx->front, htx->wrap);
+	fprintf(stderr, "\thead=%u, tail=%u - front=%u\n",
+		htx->head, htx->tail, htx->front);
 
 	for (pos = htx_get_head(htx); pos != -1; pos = htx_get_next(htx, pos)) {
 		struct htx_sl     *sl;
diff --git a/src/http_htx.c b/src/http_htx.c
index 8a407cdff..471f1ab81 100644
--- a/src/http_htx.c
+++ b/src/http_htx.c
@@ -68,12 +68,10 @@ int http_find_header(const struct htx *htx, const struct ist name,
 	struct htx_blk *blk = ctx->blk;
 	struct ist n, v;
 	enum htx_blk_type type;
-	uint32_t pos;
 
 	if (blk) {
 		char *p;
 
-		pos = htx_get_blk_pos(htx, blk);
 		if (!ctx->value.ptr)
 			goto rescan_hdr;
 		if (full)
@@ -96,15 +94,13 @@ int http_find_header(const struct htx *htx, const struct ist name,
 	if (!htx->used)
 		return 0;
 
-	pos = htx_get_head(htx);
-	while (1) {
+	for (blk = htx_get_head_blk(htx); blk; blk = htx_get_next_blk(htx, blk)) {
 	  rescan_hdr:
-		blk  = htx_get_blk(htx, pos);
 		type = htx_get_blk_type(blk);
 		if (type == HTX_BLK_EOH || type == HTX_BLK_EOM)
 			break;
 		if (type != HTX_BLK_HDR)
-			goto next_blk;
+			continue;
 		if (name.len) {
 			/* If no name was passed, we want any header. So skip the comparison */
 			n = htx_get_blk_name(htx, blk);
@@ -128,17 +124,13 @@ int http_find_header(const struct htx *htx, const struct ist name,
 			ctx->lws_after++;
 		}
 		if (!v.len)
-			goto next_blk;
+			continue;
 		ctx->blk   = blk;
 		ctx->value = v;
 		return 1;
 
 	  next_blk:
-		if (pos == htx->tail)
-			break;
-		pos++;
-		if (pos >= htx->wrap)
-			pos = 0;
+		;
 	}
 
 	ctx->blk   = NULL;
diff --git a/src/htx.c b/src/htx.c
index 9deddb15c..9f75f7afa 100644
--- a/src/htx.c
+++ b/src/htx.c
@@ -42,10 +42,8 @@ struct htx_blk *htx_defrag(struct htx *htx, struct htx_blk *blk)
 	/* start from the head */
 	for (old = htx_get_head(htx); old != -1; old = htx_get_next(htx, old)) {
 		oldblk = htx_get_blk(htx, old);
-		if (htx_get_blk_type(oldblk) == HTX_BLK_UNUSED) {
-			htx->used--;
+		if (htx_get_blk_type(oldblk) == HTX_BLK_UNUSED)
 			continue;
-		}
 
 		newblk = htx_get_blk(tmp, new);
 		newblk->addr = addr;
@@ -66,8 +64,9 @@ struct htx_blk *htx_defrag(struct htx *htx, struct htx_blk *blk)
 
 	}
 
+	htx->used = new;
 	htx->sl_off = sl_off;
-	htx->wrap = htx->used;
+	htx->head = 0;
 	htx->front = htx->tail = new - 1;
 	memcpy((void *)htx->blocks, (void *)tmp->blocks, htx->size);
 
@@ -95,8 +94,8 @@ static struct htx_blk *htx_reserve_nxblk(struct htx *htx, uint32_t blksz)
 
 	if (!htx->used) {
 		/* Empty message */
-		htx->front = htx->tail = 0;
-		htx->wrap  = htx->used = 1;
+		htx->front = htx->head = htx->tail = 0;
+		htx->used = 1;
 		blk = htx_get_blk(htx, htx->tail);
 		blk->addr = 0;
 		htx->data = blksz;
@@ -104,10 +103,10 @@ static struct htx_blk *htx_reserve_nxblk(struct htx *htx, uint32_t blksz)
 	}
 
 	used = htx->used + 1;
-	tail = htx->tail + 1;
 	prev = htx->tail;
-	wrap = htx->wrap;
-	head = htx_get_head(htx);
+	head = htx->head;
+	tail = htx->tail + 1;
+	wrap = htx_get_wrap(htx);
 
 	if (tail == wrap) {
 		frtblk = htx_get_blk(htx, htx->front);
@@ -178,7 +177,6 @@ static struct htx_blk *htx_reserve_nxblk(struct htx *htx, uint32_t blksz)
 			/* need to defragment the table before inserting upfront */
 			htx_defrag(htx, NULL);
 			frtblk = htx_get_blk(htx, htx->front);
-			wrap = htx->wrap + 1;
 			tail = htx->tail + 1;
 			used = htx->used + 1;
 			blk = htx_get_blk(htx, tail);
@@ -187,7 +185,6 @@ static struct htx_blk *htx_reserve_nxblk(struct htx *htx, uint32_t blksz)
 		}
 	}
 
-	htx->wrap  = wrap;
 	htx->tail  = tail;
 	htx->used  = used;
 	htx->data += blksz;
@@ -216,7 +213,7 @@ struct htx_blk *htx_add_blk(struct htx *htx, enum htx_blk_type type, uint32_t bl
 struct htx_blk *htx_remove_blk(struct htx *htx, struct htx_blk *blk)
 {
 	enum htx_blk_type type = htx_get_blk_type(blk);
-	uint32_t next, head, pos;
+	uint32_t next, pos, wrap;
 
 	if (type != HTX_BLK_UNUSED) {
 		/* Mark the block as unused, decrement allocated size */
@@ -228,28 +225,27 @@ struct htx_blk *htx_remove_blk(struct htx *htx, struct htx_blk *blk)
 
 	/* This is the last block in use */
 	if (htx->used == 1/* || !htx->data */) {
-		htx->front = htx->tail = 0;
-		htx->wrap  = htx->used = 0;
+		htx->front = htx->head = htx->tail = 0;
+		htx->used = 0;
 		htx->data = 0;
 		return NULL;
 	}
 
 	/* There is at least 2 blocks, so tail is always >= 0 */
 	pos  = htx_get_blk_pos(htx, blk);
-	head = htx_get_head(htx);
 	blk  = NULL;
 	next = pos + 1; /* By default retrun the next block */
-	if (htx->tail + 1 == htx->wrap) {
+	wrap = htx_get_wrap(htx);
+	if (htx->tail + 1 == wrap) {
 		/* The HTTP message doesn't wrap */
-		if (pos == head) {
-			/* remove the head, so just return the new head */
+		if (pos == htx->head) {
+			/* move the head forward */
 			htx->used--;
-			next = htx_get_head(htx);
+			htx->head++;
 		}
 		else if (pos == htx->tail) {
 			/* remove the tail. this was the last inserted block so
 			 * return NULL. */
-			htx->wrap--;
 			htx->tail--;
 			htx->used--;
 			goto end;
@@ -260,17 +256,17 @@ struct htx_blk *htx_remove_blk(struct htx *htx, struct htx_blk *blk)
 		if (pos == htx->tail) {
 			/* remove the tail. try to unwrap the message (pos == 0)
 			 * and return NULL. */
-			htx->tail = ((pos == 0) ? htx->wrap-1 : htx->tail-1);
+			htx->tail = ((pos == 0) ? wrap-1 : htx->tail-1);
 			htx->used--;
 			goto end;
 		}
-		else if (pos == head) {
-			/* remove the head, try to unwrap the message (pos+1 ==
-			 * wrap) and return the new head */
+		else if (pos == htx->head) {
+			/* move the head forward and try to unwrap the message
+			 * (head+1 == wrap) */
 			htx->used--;
-			if (pos + 1 == htx->wrap)
-				htx->wrap = htx->tail + 1;
-			next = htx_get_head(htx);
+			htx->head++;
+			if (htx->head == wrap)
+				htx->head = next = 0;
 		}
 	}
 
diff --git a/src/stream.c b/src/stream.c
index 1d2e6ce02..e6530343e 100644
--- a/src/stream.c
+++ b/src/stream.c
@@ -3295,7 +3295,7 @@ static int stats_dump_full_strm_to_buffer(struct stream_interface *si, struct st
 			chunk_appendf(&trash,
 				      "      htx=%p flags=0x%x size=%u data=%u used=%u wrap=%s extra=%llu\n",
 				      htx, htx->flags, htx->size, htx->data, htx->used,
-				      (!htx->used || htx->tail+1 == htx->wrap) ? "NO" : "YES",
+				      (htx->tail >= htx->head) ? "NO" : "YES",
 				      (unsigned long long)htx->extra);
 		}
 
@@ -3334,7 +3334,7 @@ static int stats_dump_full_strm_to_buffer(struct stream_interface *si, struct st
 			chunk_appendf(&trash,
 				      "      htx=%p flags=0x%x size=%u data=%u used=%u wrap=%s extra=%llu\n",
 				      htx, htx->flags, htx->size, htx->data, htx->used,
-				      (!htx->used || htx->tail+1 == htx->wrap) ? "NO" : "YES",
+				      (htx->tail >= htx->head) ? "NO" : "YES",
 				      (unsigned long long)htx->extra);
 		}