diff --git a/model/histogram/float_histogram.go b/model/histogram/float_histogram.go
index d3f013935c..bfb3c3d19f 100644
--- a/model/histogram/float_histogram.go
+++ b/model/histogram/float_histogram.go
@@ -218,23 +218,17 @@ func (h *FloatHistogram) Add(other *FloatHistogram) *FloatHistogram {
 	h.Count += other.Count
 	h.Sum += other.Sum
 
-	// TODO(beorn7): If needed, this can be optimized by inspecting the
-	// spans in other and create missing buckets in h in batches.
-	var iInSpan, index int32
-	for iSpan, iBucket, it := -1, -1, other.floatBucketIterator(true, h.ZeroThreshold, h.Schema); it.Next(); {
-		b := it.At()
-		h.PositiveSpans, h.PositiveBuckets, iSpan, iBucket, iInSpan = addBucket(
-			b, h.PositiveSpans, h.PositiveBuckets, iSpan, iBucket, iInSpan, index,
-		)
-		index = b.Index
-	}
-	for iSpan, iBucket, it := -1, -1, other.floatBucketIterator(false, h.ZeroThreshold, h.Schema); it.Next(); {
-		b := it.At()
-		h.NegativeSpans, h.NegativeBuckets, iSpan, iBucket, iInSpan = addBucket(
-			b, h.NegativeSpans, h.NegativeBuckets, iSpan, iBucket, iInSpan, index,
-		)
-		index = b.Index
+	otherPositiveSpans := other.PositiveSpans
+	otherPositiveBuckets := other.PositiveBuckets
+	otherNegativeSpans := other.NegativeSpans
+	otherNegativeBuckets := other.NegativeBuckets
+	if other.Schema != h.Schema {
+		otherPositiveSpans, otherPositiveBuckets = mergeToSchema(other.PositiveSpans, other.PositiveBuckets, other.Schema, h.Schema)
+		otherNegativeSpans, otherNegativeBuckets = mergeToSchema(other.NegativeSpans, other.NegativeBuckets, other.Schema, h.Schema)
 	}
+
+	h.PositiveSpans, h.PositiveBuckets = addBuckets(h.Schema, h.ZeroThreshold, false, h.PositiveSpans, h.PositiveBuckets, otherPositiveSpans, otherPositiveBuckets)
+	h.NegativeSpans, h.NegativeBuckets = addBuckets(h.Schema, h.ZeroThreshold, false, h.NegativeSpans, h.NegativeBuckets, otherNegativeSpans, otherNegativeBuckets)
 	return h
 }
 
@@ -245,25 +239,17 @@ func (h *FloatHistogram) Sub(other *FloatHistogram) *FloatHistogram {
 	h.Count -= other.Count
 	h.Sum -= other.Sum
 
-	// TODO(beorn7): If needed, this can be optimized by inspecting the
-	// spans in other and create missing buckets in h in batches.
-	var iInSpan, index int32
-	for iSpan, iBucket, it := -1, -1, other.floatBucketIterator(true, h.ZeroThreshold, h.Schema); it.Next(); {
-		b := it.At()
-		b.Count *= -1
-		h.PositiveSpans, h.PositiveBuckets, iSpan, iBucket, iInSpan = addBucket(
-			b, h.PositiveSpans, h.PositiveBuckets, iSpan, iBucket, iInSpan, index,
-		)
-		index = b.Index
-	}
-	for iSpan, iBucket, it := -1, -1, other.floatBucketIterator(false, h.ZeroThreshold, h.Schema); it.Next(); {
-		b := it.At()
-		b.Count *= -1
-		h.NegativeSpans, h.NegativeBuckets, iSpan, iBucket, iInSpan = addBucket(
-			b, h.NegativeSpans, h.NegativeBuckets, iSpan, iBucket, iInSpan, index,
-		)
-		index = b.Index
+	otherPositiveSpans := other.PositiveSpans
+	otherPositiveBuckets := other.PositiveBuckets
+	otherNegativeSpans := other.NegativeSpans
+	otherNegativeBuckets := other.NegativeBuckets
+	if other.Schema != h.Schema {
+		otherPositiveSpans, otherPositiveBuckets = mergeToSchema(other.PositiveSpans, other.PositiveBuckets, other.Schema, h.Schema)
+		otherNegativeSpans, otherNegativeBuckets = mergeToSchema(other.NegativeSpans, other.NegativeBuckets, other.Schema, h.Schema)
 	}
+
+	h.PositiveSpans, h.PositiveBuckets = addBuckets(h.Schema, h.ZeroThreshold, true, h.PositiveSpans, h.PositiveBuckets, otherPositiveSpans, otherPositiveBuckets)
+	h.NegativeSpans, h.NegativeBuckets = addBuckets(h.Schema, h.ZeroThreshold, true, h.NegativeSpans, h.NegativeBuckets, otherNegativeSpans, otherNegativeBuckets)
 	return h
 }
 
@@ -298,103 +284,6 @@ func (h *FloatHistogram) Equals(h2 *FloatHistogram) bool {
 	return true
 }
 
-// addBucket takes the "coordinates" of the last bucket that was handled and
-// adds the provided bucket after it. If a corresponding bucket exists, the
-// count is added. If not, the bucket is inserted. The updated slices and the
-// coordinates of the inserted or added-to bucket are returned.
-func addBucket(
-	b Bucket[float64],
-	spans []Span, buckets []float64,
-	iSpan, iBucket int,
-	iInSpan, index int32,
-) (
-	newSpans []Span, newBuckets []float64,
-	newISpan, newIBucket int, newIInSpan int32,
-) {
-	if iSpan == -1 {
-		// First add, check if it is before all spans.
-		if len(spans) == 0 || spans[0].Offset > b.Index {
-			// Add bucket before all others.
-			buckets = append(buckets, 0)
-			copy(buckets[1:], buckets)
-			buckets[0] = b.Count
-			if len(spans) > 0 && spans[0].Offset == b.Index+1 {
-				spans[0].Length++
-				spans[0].Offset--
-				return spans, buckets, 0, 0, 0
-			}
-			spans = append(spans, Span{})
-			copy(spans[1:], spans)
-			spans[0] = Span{Offset: b.Index, Length: 1}
-			if len(spans) > 1 {
-				// Convert the absolute offset in the formerly
-				// first span to a relative offset.
-				spans[1].Offset -= b.Index + 1
-			}
-			return spans, buckets, 0, 0, 0
-		}
-		if spans[0].Offset == b.Index {
-			// Just add to first bucket.
-			buckets[0] += b.Count
-			return spans, buckets, 0, 0, 0
-		}
-		// We are behind the first bucket, so set everything to the
-		// first bucket and continue normally.
-		iSpan, iBucket, iInSpan = 0, 0, 0
-		index = spans[0].Offset
-	}
-	deltaIndex := b.Index - index
-	for {
-		remainingInSpan := int32(spans[iSpan].Length) - iInSpan
-		if deltaIndex < remainingInSpan {
-			// Bucket is in current span.
-			iBucket += int(deltaIndex)
-			iInSpan += deltaIndex
-			buckets[iBucket] += b.Count
-			return spans, buckets, iSpan, iBucket, iInSpan
-		}
-		deltaIndex -= remainingInSpan
-		iBucket += int(remainingInSpan)
-		iSpan++
-		if iSpan == len(spans) || deltaIndex < spans[iSpan].Offset {
-			// Bucket is in gap behind previous span (or there are no further spans).
-			buckets = append(buckets, 0)
-			copy(buckets[iBucket+1:], buckets[iBucket:])
-			buckets[iBucket] = b.Count
-			if deltaIndex == 0 {
-				// Directly after previous span, extend previous span.
-				if iSpan < len(spans) {
-					spans[iSpan].Offset--
-				}
-				iSpan--
-				iInSpan = int32(spans[iSpan].Length)
-				spans[iSpan].Length++
-				return spans, buckets, iSpan, iBucket, iInSpan
-			}
-			if iSpan < len(spans) && deltaIndex == spans[iSpan].Offset-1 {
-				// Directly before next span, extend next span.
-				iInSpan = 0
-				spans[iSpan].Offset--
-				spans[iSpan].Length++
-				return spans, buckets, iSpan, iBucket, iInSpan
-			}
-			// No next span, or next span is not directly adjacent to new bucket.
-			// Add new span.
-			iInSpan = 0
-			if iSpan < len(spans) {
-				spans[iSpan].Offset -= deltaIndex + 1
-			}
-			spans = append(spans, Span{})
-			copy(spans[iSpan+1:], spans[iSpan:])
-			spans[iSpan] = Span{Length: 1, Offset: deltaIndex}
-			return spans, buckets, iSpan, iBucket, iInSpan
-		}
-		// Try start of next span.
-		deltaIndex -= spans[iSpan].Offset
-		iInSpan = 0
-	}
-}
-
 // Compact eliminates empty buckets at the beginning and end of each span, then
 // merges spans that are consecutive or at most maxEmptyBuckets apart, and
 // finally splits spans that contain more consecutive empty buckets than
@@ -1033,3 +922,133 @@ func mergeToSchema(originSpans []Span, originBuckets []float64, originSchema, ta
 
 	return targetSpans, targetBuckets
 }
+
+// addBuckets adds the buckets described by spansB/bucketsB to the buckets described by spansA/bucketsA,
+// creating missing buckets in spansA/bucketsA as needed.
+// It returns the resulting spans/buckets (which must be used instead of the original spansA/bucketsA,
+// although spansA/bucketsA might get modified by this function).
+// All buckets must use the same provided schema.
+// Buckets in spansB/bucketsB with an absolute upper limit ≤ threshold are ignored.
+// If negative is true, the buckets in spansB/bucketsB are subtracted rather than added.
+func addBuckets(
+	schema int32, threshold float64, negative bool,
+	spansA []Span, bucketsA []float64,
+	spansB []Span, bucketsB []float64,
+) ([]Span, []float64) {
+	var (
+		iSpan              int = -1
+		iBucket            int = -1
+		iInSpan            int32
+		indexA             int32
+		indexB             int32
+		bIdxB              int
+		bucketB            float64
+		deltaIndex         int32
+		lowerThanThreshold = true
+	)
+
+	for _, spanB := range spansB {
+		indexB += spanB.Offset
+		for j := 0; j < int(spanB.Length); j++ {
+			if lowerThanThreshold && getBound(indexB, schema) <= threshold {
+				goto nextLoop
+			}
+			lowerThanThreshold = false
+
+			bucketB = bucketsB[bIdxB]
+			if negative {
+				bucketB *= -1
+			}
+
+			if iSpan == -1 {
+				if len(spansA) == 0 || spansA[0].Offset > indexB {
+					// Add bucket before all others.
+					bucketsA = append(bucketsA, 0)
+					copy(bucketsA[1:], bucketsA)
+					bucketsA[0] = bucketB
+					if len(spansA) > 0 && spansA[0].Offset == indexB+1 {
+						spansA[0].Length++
+						spansA[0].Offset--
+						goto nextLoop
+					} else {
+						spansA = append(spansA, Span{})
+						copy(spansA[1:], spansA)
+						spansA[0] = Span{Offset: indexB, Length: 1}
+						if len(spansA) > 1 {
+							// Convert the absolute offset in the formerly
+							// first span to a relative offset.
+							spansA[1].Offset -= indexB + 1
+						}
+						goto nextLoop
+					}
+				} else if spansA[0].Offset == indexB {
+					// Just add to first bucket.
+					bucketsA[0] += bucketB
+					goto nextLoop
+				}
+				iSpan, iBucket, iInSpan = 0, 0, 0
+				indexA = spansA[0].Offset
+			}
+			deltaIndex = indexB - indexA
+			for {
+				remainingInSpan := int32(spansA[iSpan].Length) - iInSpan
+				if deltaIndex < remainingInSpan {
+					// Bucket is in current span.
+					iBucket += int(deltaIndex)
+					iInSpan += deltaIndex
+					bucketsA[iBucket] += bucketB
+					break
+				} else {
+					deltaIndex -= remainingInSpan
+					iBucket += int(remainingInSpan)
+					iSpan++
+					if iSpan == len(spansA) || deltaIndex < spansA[iSpan].Offset {
+						// Bucket is in gap behind previous span (or there are no further spans).
+						bucketsA = append(bucketsA, 0)
+						copy(bucketsA[iBucket+1:], bucketsA[iBucket:])
+						bucketsA[iBucket] = bucketB
+						switch {
+						case deltaIndex == 0:
+							// Directly after previous span, extend previous span.
+							if iSpan < len(spansA) {
+								spansA[iSpan].Offset--
+							}
+							iSpan--
+							iInSpan = int32(spansA[iSpan].Length)
+							spansA[iSpan].Length++
+							goto nextLoop
+						case iSpan < len(spansA) && deltaIndex == spansA[iSpan].Offset-1:
+							// Directly before next span, extend next span.
+							iInSpan = 0
+							spansA[iSpan].Offset--
+							spansA[iSpan].Length++
+							goto nextLoop
+						default:
+							// No next span, or next span is not directly adjacent to new bucket.
+							// Add new span.
+							iInSpan = 0
+							if iSpan < len(spansA) {
+								spansA[iSpan].Offset -= deltaIndex + 1
+							}
+							spansA = append(spansA, Span{})
+							copy(spansA[iSpan+1:], spansA[iSpan:])
+							spansA[iSpan] = Span{Length: 1, Offset: deltaIndex}
+							goto nextLoop
+						}
+					} else {
+						// Try start of next span.
+						deltaIndex -= spansA[iSpan].Offset
+						iInSpan = 0
+					}
+				}
+			}
+
+		nextLoop:
+			indexA = indexB
+			indexB++
+			bIdxB++
+		}
+	}
+
+	return spansA, bucketsA
+}