diff --git a/go.mod b/go.mod
index 01889fd320..5a90a7c536 100644
--- a/go.mod
+++ b/go.mod
@@ -53,6 +53,7 @@ require (
 	go.uber.org/goleak v1.3.0
 	go.uber.org/mock v0.6.0
 	go.yaml.in/yaml/v4 v4.0.0-rc.4
+	golang.org/x/net v0.51.0
 	golang.org/x/sync v0.20.0
 	golang.org/x/sys v0.44.0
 	google.golang.org/grpc v1.81.1
@@ -136,7 +137,6 @@ require (
 	go.opentelemetry.io/proto/otlp v1.9.0 // indirect
 	go.yaml.in/yaml/v3 v3.0.4 // indirect
 	golang.org/x/crypto v0.48.0 // indirect
-	golang.org/x/net v0.51.0 // indirect
 	golang.org/x/term v0.41.0 // indirect
 	golang.org/x/text v0.34.0 // indirect
 	golang.org/x/time v0.14.0 // indirect
diff --git a/internal/desktop/proxy.go b/internal/desktop/proxy.go
index 0f2af1d0f0..7b45fbefcb 100644
--- a/internal/desktop/proxy.go
+++ b/internal/desktop/proxy.go
@@ -27,10 +27,18 @@ import (
 
 	"github.com/moby/moby/client"
 	"github.com/sirupsen/logrus"
+	"golang.org/x/net/http/httpproxy"
 
 	"github.com/docker/compose/v5/internal/memnet"
 )
 
+// ddProxyHost is a sentinel hostname stamped into the proxy URL handed to the
+// stdlib transport. It is never resolved on the network: the transport's
+// DialContext recognizes it and routes the connection to Docker Desktop's
+// proxy socket instead. The .invalid TLD is reserved (RFC 6761) so it can
+// never collide with a real registry host.
+const ddProxyHost = "docker-desktop-http-proxy.invalid"
+
 // Endpoint returns the Docker Desktop API socket endpoint advertised via the
 // engine info labels, or "" when the active engine is not Docker Desktop.
 func Endpoint(ctx context.Context, apiClient client.APIClient) (string, error) {
@@ -51,8 +59,8 @@ func Endpoint(ctx context.Context, apiClient client.APIClient) (string, error) {
 // when the input is not a recognized form or when the derived unix socket
 // does not exist (older DD versions or non-DD installs).
 //
-// On macOS/Linux: unix:///path/to/Data/docker-cli.sock      → unix:///path/to/Data/httpproxy.sock
-// On Windows:    npipe://./pipe/dockerDesktopLinuxEngine    → npipe://./pipe/dockerHttpProxy
+// On macOS/Linux: unix:///path/to/Data/docker-cli.sock     → unix:///path/to/Data/httpproxy.sock
+// On Windows:    npipe://\\.\pipe\docker_cli               → npipe://\\.\pipe\dockerHttpProxy
 func httpProxySocketEndpoint(endpoint string) string {
 	if sockPath, ok := strings.CutPrefix(endpoint, "unix://"); ok {
 		proxyPath := filepath.Join(filepath.Dir(sockPath), "httpproxy.sock")
@@ -62,7 +70,20 @@ func httpProxySocketEndpoint(endpoint string) string {
 		return "unix://" + proxyPath
 	}
 	if strings.HasPrefix(endpoint, "npipe://") {
-		return "npipe://./pipe/dockerHttpProxy"
+		// Named pipes all live in the same `\\.\pipe\` namespace, so only the
+		// trailing pipe name differs. Swap it in place rather than rebuilding
+		// the endpoint string: this preserves the engine endpoint's exact
+		// prefix (Docker Desktop reports the backslash form
+		// `npipe://\\.\pipe\docker_cli`), which winio can dial. Hardcoding
+		// `npipe://./pipe/...` instead would yield the relative path
+		// `./pipe/dockerHttpProxy`, which fails with "open
+		// ./pipe/dockerHttpProxy: The system cannot find the path specified."
+		// (docker/compose#13824). LastIndexAny handles both the backslash form
+		// above and the forward-slash form `npipe:////./pipe/...`.
+		if idx := strings.LastIndexAny(endpoint, `/\`); idx >= 0 {
+			return endpoint[:idx+1] + "dockerHttpProxy"
+		}
+		return ""
 	}
 	return ""
 }
@@ -74,6 +95,11 @@ func httpProxySocketEndpoint(endpoint string) string {
 // built-in transport). Pass "" for endpoint when DD is not the active
 // engine.
 //
+// Loopback targets (localhost, 127.0.0.0/8, ::1) and any host matched by the
+// NO_PROXY environment variable bypass the proxy and connect directly, so
+// `compose publish` to a local/insecure registry behaves like `docker push`
+// instead of failing inside the proxy (docker/compose#13824).
+//
 // When DD is available, the returned transport is a clone of
 // http.DefaultTransport with only Proxy and DialContext overridden, so it
 // preserves stdlib timeout, pooling, and HTTP/2 defaults.
@@ -95,13 +121,49 @@ func ProxyTransport(endpoint string) http.RoundTripper {
 	} else {
 		tr = &http.Transport{}
 	}
-	tr.Proxy = http.ProxyURL(&url.URL{Scheme: "http"})
-	tr.DialContext = func(ctx context.Context, _, _ string) (net.Conn, error) {
-		return memnet.DialEndpoint(ctx, proxyEndpoint)
+
+	tr.Proxy = ddProxyFunc()
+
+	// Bypassed (direct) requests reach DialContext with their real target
+	// address and use the standard dialer; proxied requests reach it with the
+	// sentinel proxy address and are routed to the Docker Desktop socket.
+	baseDial := tr.DialContext
+	if baseDial == nil {
+		baseDial = (&net.Dialer{}).DialContext
+	}
+	proxyAddr := net.JoinHostPort(ddProxyHost, "80")
+	tr.DialContext = func(ctx context.Context, network, addr string) (net.Conn, error) {
+		if addr == proxyAddr {
+			return memnet.DialEndpoint(ctx, proxyEndpoint)
+		}
+		return baseDial(ctx, network, addr)
 	}
 	return tr
 }
 
+// ddProxyFunc returns a transport Proxy function that selects the Docker
+// Desktop proxy for every request except loopback targets and hosts excluded
+// via NO_PROXY, which connect directly. It piggybacks on
+// httpproxy.Config.ProxyFunc, which already exempts localhost and loopback
+// addresses; the sentinel proxy URL is only used so that non-exempt requests
+// resolve to ddProxyHost, which DialContext intercepts.
+func ddProxyFunc() func(*http.Request) (*url.URL, error) {
+	proxyURL := (&url.URL{Scheme: "http", Host: ddProxyHost}).String()
+	noProxy := os.Getenv("NO_PROXY")
+	if noProxy == "" {
+		noProxy = os.Getenv("no_proxy")
+	}
+	cfg := &httpproxy.Config{
+		HTTPProxy:  proxyURL,
+		HTTPSProxy: proxyURL,
+		NoProxy:    noProxy,
+	}
+	proxyFunc := cfg.ProxyFunc()
+	return func(req *http.Request) (*url.URL, error) {
+		return proxyFunc(req.URL)
+	}
+}
+
 // ProxyTransportFor discovers the Docker Desktop endpoint via apiClient and
 // returns the matching transport, or nil when DD is not active or discovery
 // fails (so callers fall back to their own default transport).
diff --git a/internal/desktop/proxy_test.go b/internal/desktop/proxy_test.go
index 460ec4181e..de97d5ae4b 100644
--- a/internal/desktop/proxy_test.go
+++ b/internal/desktop/proxy_test.go
@@ -48,8 +48,33 @@ func TestHTTPProxySocketEndpoint_UnixSocketMissing(t *testing.T) {
 }
 
 func TestHTTPProxySocketEndpoint_WindowsNamedPipe(t *testing.T) {
-	got := httpProxySocketEndpoint("npipe://./pipe/dockerCli")
-	assert.Equal(t, got, "npipe://./pipe/dockerHttpProxy")
+	// The derived proxy endpoint must keep the engine endpoint's exact prefix
+	// and only swap the trailing pipe name, so the result stays dialable by
+	// winio (docker/compose#13824).
+	cases := []struct {
+		name     string
+		endpoint string
+		want     string
+	}{
+		{
+			// The form Docker Desktop actually reports (observed on DD 29.5.2):
+			// backslash `\\.\pipe\` namespace.
+			name:     "backslash form (real Docker Desktop)",
+			endpoint: `npipe://\\.\pipe\docker_cli`,
+			want:     `npipe://\\.\pipe\dockerHttpProxy`,
+		},
+		{
+			// Forward-slash form some tooling uses; must work too.
+			name:     "forward-slash form",
+			endpoint: "npipe:////./pipe/dockerDesktopLinuxEngine",
+			want:     "npipe:////./pipe/dockerHttpProxy",
+		},
+	}
+	for _, tc := range cases {
+		t.Run(tc.name, func(t *testing.T) {
+			assert.Equal(t, httpProxySocketEndpoint(tc.endpoint), tc.want)
+		})
+	}
 }
 
 func TestHTTPProxySocketEndpoint_EmptyOrUnknown(t *testing.T) {
@@ -99,6 +124,44 @@ func TestProxyTransport_RoutesThroughDockerDesktop(t *testing.T) {
 	assert.Equal(t, tr.ForceAttemptHTTP2, src.ForceAttemptHTTP2)
 }
 
+// TestDDProxyFunc_BypassesLoopbackAndHonorsNoProxy exercises the proxy
+// selection directly (rather than through ProxyTransport, which needs a live
+// socket) so it runs on every platform, including Windows. This is the core of
+// the docker/compose#13824 fix: loopback and NO_PROXY targets must connect
+// directly instead of being forced through the Docker Desktop proxy.
+func TestDDProxyFunc_BypassesLoopbackAndHonorsNoProxy(t *testing.T) {
+	t.Setenv("NO_PROXY", "registry.internal")
+	t.Setenv("no_proxy", "registry.internal")
+
+	proxyFunc := ddProxyFunc()
+
+	cases := []struct {
+		name      string
+		reqURL    string
+		wantProxy bool
+	}{
+		{"loopback name", "http://localhost:5000/v2/", false},
+		{"loopback IPv4", "http://127.0.0.1:5000/v2/", false},
+		{"no_proxy host", "https://registry.internal/v2/", false},
+		{"external https", "https://registry-1.docker.io/v2/", true},
+		{"external http", "http://example.com/v2/", true},
+	}
+	for _, tc := range cases {
+		t.Run(tc.name, func(t *testing.T) {
+			req, err := http.NewRequest(http.MethodGet, tc.reqURL, http.NoBody)
+			assert.NilError(t, err)
+			proxyURL, err := proxyFunc(req)
+			assert.NilError(t, err)
+			if tc.wantProxy {
+				assert.Assert(t, proxyURL != nil, "expected %s to route through the Docker Desktop proxy", tc.reqURL)
+				assert.Equal(t, proxyURL.Host, ddProxyHost)
+			} else {
+				assert.Assert(t, proxyURL == nil, "expected %s to bypass the proxy and connect directly", tc.reqURL)
+			}
+		})
+	}
+}
+
 func mustTouch(t *testing.T, path string) {
 	t.Helper()
 	f, err := os.Create(path)