diff --git a/internal/pmtud/icmp/errors.go b/internal/pmtud/icmp/errors.go
index 277c5551..4a9c3e97 100644
--- a/internal/pmtud/icmp/errors.go
+++ b/internal/pmtud/icmp/errors.go
@@ -4,7 +4,6 @@ import (
 	"context"
 	"errors"
 	"fmt"
-	"net"
 	"strings"
 	"time"
 )
@@ -15,6 +14,7 @@ var (
 	ErrCommunicationAdministrativelyProhibited = errors.New("communication administratively prohibited")
 	ErrBodyUnsupported                         = errors.New("ICMP body type is not supported")
 	ErrMTUNotFound                             = errors.New("MTU not found")
+	errTimeout                                 = errors.New("operation timed out")
 )
 
 func wrapConnErr(err error, timedCtx context.Context, pingTimeout time.Duration) error { //nolint:revive
@@ -22,7 +22,7 @@ func wrapConnErr(err error, timedCtx context.Context, pingTimeout time.Duration)
 	case strings.HasSuffix(err.Error(), "sendto: operation not permitted"):
 		err = fmt.Errorf("%w", ErrNotPermitted)
 	case errors.Is(timedCtx.Err(), context.DeadlineExceeded):
-		err = fmt.Errorf("%w (timed out after %s)", net.ErrClosed, pingTimeout)
+		err = fmt.Errorf("%w: after %s", errTimeout, pingTimeout)
 	case timedCtx.Err() != nil:
 		err = timedCtx.Err()
 	}
diff --git a/internal/pmtud/icmp/icmp.go b/internal/pmtud/icmp/icmp.go
index 8e9b9acb..07043060 100644
--- a/internal/pmtud/icmp/icmp.go
+++ b/internal/pmtud/icmp/icmp.go
@@ -4,7 +4,6 @@ import (
 	"context"
 	"errors"
 	"fmt"
-	"net"
 	"net/netip"
 	"time"
 
@@ -26,7 +25,7 @@ func PathMTUDiscover(ctx context.Context, ip netip.Addr,
 		switch {
 		case err == nil:
 			return mtu, nil
-		case errors.Is(err, net.ErrClosed) || errors.Is(err, ErrCommunicationAdministrativelyProhibited): // blackhole
+		case errors.Is(err, errTimeout) || errors.Is(err, ErrCommunicationAdministrativelyProhibited): // blackhole
 		default:
 			return 0, fmt.Errorf("finding IPv4 next hop MTU: %w", err)
 		}
@@ -36,7 +35,7 @@ func PathMTUDiscover(ctx context.Context, ip netip.Addr,
 		switch {
 		case err == nil:
 			return mtu, nil
-		case errors.Is(err, net.ErrClosed): // blackhole
+		case errors.Is(err, errTimeout): // blackhole
 		default:
 			return 0, fmt.Errorf("getting IPv6 packet-too-big message: %w", err)
 		}