diff --git a/pkg/util/log/log_bridge.go b/pkg/util/log/log_bridge.go
index 09ae9c253cc1..fe6f299eaf54 100644
--- a/pkg/util/log/log_bridge.go
+++ b/pkg/util/log/log_bridge.go
@@ -16,13 +16,19 @@ import (
 	"fmt"
 	stdLog "log"
 	"strconv"
+	"strings"
 )
 
 // NewStdLogger creates a *stdLog.Logger that forwards messages to the
 // CockroachDB logs with the specified severity.
 //
-// The prefix appears at the beginning of each generated log line.
+// The prefix should be the path of the package for which this logger
+// is used. The prefix will be concatenated directly with the name
+// of the file that triggered the logging.
 func NewStdLogger(severity Severity, prefix string) *stdLog.Logger {
+	if prefix != "" && !strings.HasSuffix(prefix, "/") {
+		prefix += "/"
+	}
 	return stdLog.New(logBridge(severity), prefix, stdLog.Lshortfile)
 }
 
@@ -67,7 +73,9 @@ func (lb logBridge) Write(b []byte) (n int, err error) {
 	if parts := bytes.SplitN(b, []byte{':'}, 3); len(parts) != 3 || len(parts[0]) < 1 || len(parts[2]) < 1 {
 		entry.Message = fmt.Sprintf("bad log format: %s", b)
 	} else {
-		entry.File = string(parts[0])
+		// We use a "(gostd)" prefix so that these log lines correctly point
+		// to the go standard library instead of our own source directory.
+		entry.File = "(gostd) " + string(parts[0])
 		entry.Message = string(parts[2][1 : len(parts[2])-1]) // skip leading space and trailing newline
 		entry.Line, err = strconv.ParseInt(string(parts[1]), 10, 64)
 		if err != nil {
diff --git a/pkg/util/netutil/net.go b/pkg/util/netutil/net.go
index 3a852fa064dd..aad4514fd561 100644
--- a/pkg/util/netutil/net.go
+++ b/pkg/util/netutil/net.go
@@ -54,7 +54,7 @@ func ListenAndServeGRPC(
 	return ln, nil
 }
 
-var httpLogger = log.NewStdLogger(log.Severity_ERROR, "httpLogger")
+var httpLogger = log.NewStdLogger(log.Severity_ERROR, "net/http")
 
 // Server is a thin wrapper around http.Server. See MakeServer for more detail.
 type Server struct {