diff --git a/wal/wal.go b/wal/wal.go
index 0e95ba2a..80a28248 100644
--- a/wal/wal.go
+++ b/wal/wal.go
@@ -261,6 +261,8 @@ func (w *WAL) Repair(err error) error {
 	// But that's not generally applicable if the records have any kind of causality.
 	// Maybe as an extra mode in the future if mid-WAL corruptions become
 	// a frequent concern.
+	err = errors.Cause(err) // So that we can pick up errors even if wrapped.
+
 	cerr, ok := err.(*CorruptionErr)
 	if !ok {
 		return errors.New("cannot handle error")
diff --git a/wal/wal_test.go b/wal/wal_test.go
index d1b724c7..26ee8663 100644
--- a/wal/wal_test.go
+++ b/wal/wal_test.go
@@ -23,6 +23,7 @@ import (
 	"os"
 	"testing"
 
+	"github.com/pkg/errors"
 	"github.com/prometheus/tsdb/testutil"
 )
 
@@ -286,8 +287,8 @@ func TestWAL_Repair(t *testing.T) {
 			for r.Next() {
 			}
 			testutil.NotOk(t, r.Err())
-
 			testutil.Ok(t, w.Repair(r.Err()))
+			testutil.Ok(t, w.Repair(errors.Wrap(r.Err(), "err"))) // See https://github.com/prometheus/prometheus/issues/4603
 
 			sr, err = NewSegmentsReader(dir)
 			testutil.Ok(t, err)