diff --git a/include/haproxy/freq_ctr.h b/include/haproxy/freq_ctr.h
index 6ddcde842..dfb187483 100644
--- a/include/haproxy/freq_ctr.h
+++ b/include/haproxy/freq_ctr.h
@@ -31,7 +31,7 @@
 ullong _freq_ctr_total_from_values(uint period, int pend, uint tick, ullong past, ullong curr);
 ullong freq_ctr_total(const struct freq_ctr *ctr, uint period, int pend);
 ullong freq_ctr_total_estimate(const struct freq_ctr *ctr, uint period, int pend);
-int freq_ctr_overshoot_period(const struct freq_ctr *ctr, uint period, uint freq);
+uint freq_ctr_overshoot_period(const struct freq_ctr *ctr, uint period, uint freq);
 uint update_freq_ctr_period_slow(struct freq_ctr *ctr, uint period, uint inc);
 
 /* Only usable during single threaded startup phase. */
diff --git a/src/flt_bwlim.c b/src/flt_bwlim.c
index 0ca768091..ebb33a5f1 100644
--- a/src/flt_bwlim.c
+++ b/src/flt_bwlim.c
@@ -79,9 +79,9 @@ static int bwlim_apply_limit(struct filter *filter, struct channel *chn, unsigne
 	struct bwlim_state *st = filter->ctx;
 	struct freq_ctr *bytes_rate;
 	uint64_t remain;
-	unsigned int period, limit, tokens, users, factor;
+	unsigned int period, limit, tokens, users, factor, overshoot;
 	unsigned int wait = 0;
-	int overshoot, ret = 0;
+	int ret = 0;
 
 	/* Don't forward anything if there is nothing to forward or the waiting
 	 * time is not expired
diff --git a/src/freq_ctr.c b/src/freq_ctr.c
index f072ce554..205e43147 100644
--- a/src/freq_ctr.c
+++ b/src/freq_ctr.c
@@ -184,17 +184,17 @@ ullong freq_ctr_total_estimate(const struct freq_ctr *ctr, uint period, int pend
 	return _freq_ctr_total_from_values(period, pend, tick, past, curr);
 }
 
-/* Returns the excess of events (may be negative) over the current period for
- * target frequency <freq>. It returns 0 if the counter is in the future or if
- * the counter is empty. The result considers the position of the current time
- * within the current period.
+/* Returns the excess of events over the current period for target frequency
+ * <freq>. It returns 0 if the counter is in the future or if the counter is
+ * empty. The result considers the position of the current time within the
+ * current period.
  *
- * The caller may safely add new events if result is negative or null.
+ * The caller may safely add new events if result is zero.
  */
-int freq_ctr_overshoot_period(const struct freq_ctr *ctr, uint period, uint freq)
+uint freq_ctr_overshoot_period(const struct freq_ctr *ctr, uint period, uint freq)
 {
 	ullong curr, old_curr;
-	uint tick, old_tick;
+	uint tick, old_tick, linear_usage;
 	int elapsed;
 
 	tick = HA_ATOMIC_LOAD(&ctr->curr_tick);
@@ -245,7 +245,12 @@ int freq_ctr_overshoot_period(const struct freq_ctr *ctr, uint period, uint freq
 		return 0;
 	}
 
-	return curr - div64_32((uint64_t)elapsed * freq, period);
+	linear_usage = div64_32((uint64_t)elapsed * freq, period);
+	if (curr < linear_usage) {
+		/* The counter is below a uniform linear increase across the period, no overshoot */
+		return 0;
+	}
+	return curr - linear_usage;
 }
 
 /*