diff --git a/mem/buffer_pool.go b/mem/buffer_pool.go
index f211e727451f..e37afdd1981d 100644
--- a/mem/buffer_pool.go
+++ b/mem/buffer_pool.go
@@ -38,9 +38,11 @@ type BufferPool interface {
 	Put(*[]byte)
 }
 
+const goPageSize = 4 << 10 // 4KiB. N.B. this must be a power of 2.
+
 var defaultBufferPoolSizes = []int{
 	256,
-	4 << 10,  // 4KB (go page size)
+	goPageSize,
 	16 << 10, // 16KB (max HTTP/2 frame size used by gRPC)
 	32 << 10, // 32KB (default buffer size for io.Copy)
 	1 << 20,  // 1MB
@@ -172,7 +174,14 @@ func (p *simpleBufferPool) Get(size int) *[]byte {
 		p.pool.Put(bs)
 	}
 
-	b := make([]byte, size)
+	// If we're going to allocate, round up to the nearest page. This way if
+	// requests frequently arrive with small variation we don't allocate
+	// repeatedly if we get unlucky and they increase over time. By default we
+	// only allocate here if size > 1MiB. Because goPageSize is a power of 2, we
+	// can round up efficiently.
+	allocSize := (size + goPageSize - 1) & ^(goPageSize - 1)
+
+	b := make([]byte, size, allocSize)
 	return &b
 }