diff --git a/pgconn/pgconn.go b/pgconn/pgconn.go
index abf6c9d8d..45b6362da 100644
--- a/pgconn/pgconn.go
+++ b/pgconn/pgconn.go
@@ -292,7 +292,13 @@ func connectPreferred(ctx context.Context, config *Config, connectOneConfigs []*
 	}
 
 	if fallbackConnectOneConfig != nil {
-		pgConn, err := connectOne(ctx, config, fallbackConnectOneConfig, true)
+		fallbackCtx := octx
+		if config.ConnectTimeout != 0 {
+			var cancel context.CancelFunc
+			fallbackCtx, cancel = context.WithTimeout(octx, config.ConnectTimeout)
+			defer cancel()
+		}
+		pgConn, err := connectOne(fallbackCtx, config, fallbackConnectOneConfig, true)
 		if err == nil {
 			return pgConn, nil
 		}