diff --git a/.golangci.yml b/.golangci.yml
index 0e8f82b543..ec9005be92 100644
--- a/.golangci.yml
+++ b/.golangci.yml
@@ -156,12 +156,6 @@ issues:
       linters:
         - staticcheck
 
-    # FIXME temporarily suppress these until they are moved internal to container/streams.
-    - text: "SA1019: ioutils\\.(ErrClosed|BytesPipe|NewBytesPipe)"
-      path: "container/stream/"
-      linters:
-        - staticcheck
-
     - text: "ineffectual assignment to ctx"
       source: "ctx[, ].*=.*\\(ctx[,)]"
       linters:
diff --git a/pkg/ioutils/buffer.go b/container/stream/bytespipe/buffer.go
similarity index 92%
rename from pkg/ioutils/buffer.go
rename to container/stream/bytespipe/buffer.go
index 466f79294b..3beae1350f 100644
--- a/pkg/ioutils/buffer.go
+++ b/container/stream/bytespipe/buffer.go
@@ -1,4 +1,4 @@
-package ioutils // import "github.com/docker/docker/pkg/ioutils"
+package bytespipe
 
 import (
 	"errors"
diff --git a/pkg/ioutils/buffer_test.go b/container/stream/bytespipe/buffer_test.go
similarity index 97%
rename from pkg/ioutils/buffer_test.go
rename to container/stream/bytespipe/buffer_test.go
index aa75bab48a..2a849029ce 100644
--- a/pkg/ioutils/buffer_test.go
+++ b/container/stream/bytespipe/buffer_test.go
@@ -1,4 +1,4 @@
-package ioutils // import "github.com/docker/docker/pkg/ioutils"
+package bytespipe
 
 import (
 	"bytes"
diff --git a/pkg/ioutils/bytespipe.go b/container/stream/bytespipe/bytespipe.go
similarity index 90%
rename from pkg/ioutils/bytespipe.go
rename to container/stream/bytespipe/bytespipe.go
index 85450bf6b3..60390fdf71 100644
--- a/pkg/ioutils/bytespipe.go
+++ b/container/stream/bytespipe/bytespipe.go
@@ -1,4 +1,4 @@
-package ioutils // import "github.com/docker/docker/pkg/ioutils"
+package bytespipe
 
 import (
 	"errors"
@@ -18,8 +18,6 @@ const blockThreshold = 1e6
 
 var (
 	// ErrClosed is returned when Write is called on a closed BytesPipe.
-	//
-	// Deprecated: this type is only used internally, and will be removed in the next release.
 	ErrClosed = errors.New("write to closed BytesPipe")
 
 	bufPools     = make(map[int]*sync.Pool)
@@ -30,8 +28,6 @@ var (
 // All written data may be read at most once. Also, BytesPipe allocates
 // and releases new byte slices to adjust to current needs, so the buffer
 // won't be overgrown after peak loads.
-//
-// Deprecated: this type is only used internally, and will be removed in the next release.
 type BytesPipe struct {
 	mu        sync.Mutex
 	wait      *sync.Cond
@@ -41,12 +37,10 @@ type BytesPipe struct {
 	readBlock bool  // check read BytesPipe is Wait() or not
 }
 
-// NewBytesPipe creates new BytesPipe, initialized by specified slice.
+// New creates new BytesPipe, initialized by specified slice.
 // If buf is nil, then it will be initialized with slice which cap is 64.
 // buf will be adjusted in a way that len(buf) == 0, cap(buf) == cap(buf).
-//
-// Deprecated: this function is only used internally, and will be removed in the next release.
-func NewBytesPipe() *BytesPipe {
+func New() *BytesPipe {
 	bp := &BytesPipe{}
 	bp.buf = append(bp.buf, getBuffer(minCap))
 	bp.wait = sync.NewCond(&bp.mu)
diff --git a/pkg/ioutils/bytespipe_test.go b/container/stream/bytespipe/bytespipe_test.go
similarity index 95%
rename from pkg/ioutils/bytespipe_test.go
rename to container/stream/bytespipe/bytespipe_test.go
index 31197b6529..58a71c574f 100644
--- a/pkg/ioutils/bytespipe_test.go
+++ b/container/stream/bytespipe/bytespipe_test.go
@@ -1,4 +1,4 @@
-package ioutils // import "github.com/docker/docker/pkg/ioutils"
+package bytespipe
 
 import (
 	"crypto/sha256"
@@ -9,7 +9,7 @@ import (
 )
 
 func TestBytesPipeRead(t *testing.T) {
-	buf := NewBytesPipe()
+	buf := New()
 	_, _ = buf.Write([]byte("12"))
 	_, _ = buf.Write([]byte("34"))
 	_, _ = buf.Write([]byte("56"))
@@ -49,7 +49,7 @@ func TestBytesPipeRead(t *testing.T) {
 }
 
 func TestBytesPipeWrite(t *testing.T) {
-	buf := NewBytesPipe()
+	buf := New()
 	_, _ = buf.Write([]byte("12"))
 	_, _ = buf.Write([]byte("34"))
 	_, _ = buf.Write([]byte("56"))
@@ -62,7 +62,7 @@ func TestBytesPipeWrite(t *testing.T) {
 
 // Regression test for #41941.
 func TestBytesPipeDeadlock(t *testing.T) {
-	bp := NewBytesPipe()
+	bp := New()
 	bp.buf = []*fixedBuffer{getBuffer(blockThreshold)}
 
 	rd := make(chan error)
@@ -145,7 +145,7 @@ func TestBytesPipeWriteRandomChunks(t *testing.T) {
 		expected := hex.EncodeToString(hash.Sum(nil))
 
 		// write/read through buffer
-		buf := NewBytesPipe()
+		buf := New()
 		hash.Reset()
 
 		done := make(chan struct{})
@@ -186,7 +186,7 @@ func BenchmarkBytesPipeWrite(b *testing.B) {
 	testData := []byte("pretty short line, because why not?")
 	for i := 0; i < b.N; i++ {
 		readBuf := make([]byte, 1024)
-		buf := NewBytesPipe()
+		buf := New()
 		go func() {
 			var err error
 			for err == nil {
@@ -205,7 +205,7 @@ func BenchmarkBytesPipeRead(b *testing.B) {
 	rd := make([]byte, 512)
 	for i := 0; i < b.N; i++ {
 		b.StopTimer()
-		buf := NewBytesPipe()
+		buf := New()
 		for j := 0; j < 500; j++ {
 			_, _ = buf.Write(make([]byte, 1024))
 		}
diff --git a/container/stream/streams.go b/container/stream/streams.go
index 280cafe279..371006b64e 100644
--- a/container/stream/streams.go
+++ b/container/stream/streams.go
@@ -9,6 +9,7 @@ import (
 
 	"github.com/containerd/containerd/cio"
 	"github.com/containerd/log"
+	"github.com/docker/docker/container/stream/bytespipe"
 	"github.com/docker/docker/pkg/ioutils"
 	"github.com/docker/docker/pkg/pools"
 )
@@ -64,7 +65,7 @@ func (c *Config) StdinPipe() io.WriteCloser {
 // It adds this new out pipe to the Stdout broadcaster.
 // This will block stdout if unconsumed.
 func (c *Config) StdoutPipe() io.ReadCloser {
-	bytesPipe := ioutils.NewBytesPipe()
+	bytesPipe := bytespipe.New()
 	c.stdout.Add(bytesPipe)
 	return bytesPipe
 }
@@ -73,7 +74,7 @@ func (c *Config) StdoutPipe() io.ReadCloser {
 // It adds this new err pipe to the Stderr broadcaster.
 // This will block stderr if unconsumed.
 func (c *Config) StderrPipe() io.ReadCloser {
-	bytesPipe := ioutils.NewBytesPipe()
+	bytesPipe := bytespipe.New()
 	c.stderr.Add(bytesPipe)
 	return bytesPipe
 }