diff --git a/CHANGELOG.md b/CHANGELOG.md
index 93c84731..622d65a9 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,6 +7,10 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ## [Unreleased]
 
+### Changed
+
+- Ignore errors like `tls: failed to send closeNotify alert (but connection was closed anyway)` when closing listeners. [PR #1216](https://github.com/riverqueue/river/pull/1216).
+
 ### Fixed
 
 - Fixed leader election to track explicit database-issued leadership terms, reducing handoff flakiness and same-client reacquisition edge cases while making reelection and resign target the current leadership lease instead of a stale one. [PR #1213](https://github.com/riverqueue/river/pull/1213).
diff --git a/internal/notifier/notifier.go b/internal/notifier/notifier.go
index 8f9618c9..1df73cd3 100644
--- a/internal/notifier/notifier.go
+++ b/internal/notifier/notifier.go
@@ -7,6 +7,7 @@ import (
 	"fmt"
 	"log/slog"
 	"slices"
+	"strings"
 	"sync"
 	"time"
 
@@ -262,7 +263,7 @@ func (n *Notifier) listenerClose(ctx context.Context, skipLock bool) {
 
 	n.Logger.DebugContext(ctx, n.Name+": Listener closing")
 	if err := n.listener.Close(ctx); err != nil {
-		if !errors.Is(err, context.Canceled) {
+		if shouldIgnoreListenerError(err) {
 			n.Logger.ErrorContext(ctx, n.Name+": Error closing listener", "err", err)
 		}
 	}
@@ -270,6 +271,32 @@ func (n *Notifier) listenerClose(ctx context.Context, skipLock bool) {
 	n.isConnected = false
 }
 
+// shouldIgnoreListenerError returns true if the error is a certain type of
+// common error that we see when trying to close a listener.
+//
+// It's probably not strictly necessary to log errors on listener close, but it
+// seems not ideal to ignore them completely either. If this function were ever
+// to become to unwieldy though, we might want to go back to the drawing board.
+func shouldIgnoreListenerError(err error) bool {
+	if errors.Is(err, context.Canceled) {
+		return true
+	}
+
+	// In practice, this occurs a fair bit in some systems. See:
+	//
+	//     https://github.com/riverqueue/river/issues/256
+	//
+	// There's been an issue opened to make this a well-known error type, but
+	// it's not right now:
+	//
+	//     https://github.com/golang/go/issues/75600
+	if strings.Contains(err.Error(), "tls: failed to send closeNotify alert") {
+		return true
+	}
+
+	return false
+}
+
 const listenerTimeout = 10 * time.Second
 
 func (n *Notifier) listenerConnect(ctx context.Context, skipLock bool) error {
diff --git a/internal/notifier/notifier_test.go b/internal/notifier/notifier_test.go
index d98ff40d..a6dc16ab 100644
--- a/internal/notifier/notifier_test.go
+++ b/internal/notifier/notifier_test.go
@@ -671,6 +671,34 @@ func topicAndPayloadNotifyFunc(notifyChan chan TopicAndPayload) NotifyFunc {
 	}
 }
 
+func TestShouldIgnoreListenerError(t *testing.T) {
+	t.Parallel()
+
+	t.Run("ContextCanceled", func(t *testing.T) {
+		t.Parallel()
+
+		require.True(t, shouldIgnoreListenerError(context.Canceled))
+	})
+
+	t.Run("WrappedContextCanceled", func(t *testing.T) {
+		t.Parallel()
+
+		require.True(t, shouldIgnoreListenerError(fmt.Errorf("wrapped: %w", context.Canceled)))
+	})
+
+	t.Run("TLSCloseNotifyAlert", func(t *testing.T) {
+		t.Parallel()
+
+		require.True(t, shouldIgnoreListenerError(errors.New("tls: failed to send closeNotify alert (but connection was closed anyway): write tcp 10.0.5.131:40192->10.0.7.96:5432: i/o timeout")))
+	})
+
+	t.Run("ArbitraryError", func(t *testing.T) {
+		t.Parallel()
+
+		require.False(t, shouldIgnoreListenerError(errors.New("some other error")))
+	})
+}
+
 func sendNotification(ctx context.Context, t *testing.T, exec riverdriver.Executor, schema, topic string, payload string) {
 	t.Helper()