diff --git a/cmd/root.go b/cmd/root.go
index b252dd6c..0f2b5a8f 100644
--- a/cmd/root.go
+++ b/cmd/root.go
@@ -566,6 +566,9 @@ the Proxy will then pick-up automatically.`)
 	localFlags.Uint64Var(&c.conf.MaxConnections, "max-connections", 0,
 		`Limits the number of connections by refusing any additional connections.
 When this flag is not set, there is no limit.`)
+	localFlags.DurationVar(&c.conf.WaitBeforeClose, "min-sigterm-delay", 0,
+	`The number of seconds to accept new connections after receiving a TERM
+signal. Defaults to 0s.`)
 	localFlags.DurationVar(&c.conf.WaitOnClose, "max-sigterm-delay", 0,
 		`Maximum amount of time to wait after for any open connections
 to close after receiving a TERM signal. The proxy will shut
@@ -1179,8 +1182,10 @@ func runSignalWrapper(cmd *Command) (err error) {
 	switch {
 	case errors.Is(err, errSigInt):
 		cmd.logger.Infof("SIGINT signal received. Shutting down...")
+		time.Sleep(cmd.conf.WaitBeforeClose)
 	case errors.Is(err, errSigTerm):
 		cmd.logger.Infof("SIGTERM signal received. Shutting down...")
+		time.Sleep(cmd.conf.WaitBeforeClose)
 	default:
 		cmd.logger.Errorf("The proxy has encountered a terminal error: %v", err)
 	}
diff --git a/cmd/root_test.go b/cmd/root_test.go
index 0a64dba4..00cf87d6 100644
--- a/cmd/root_test.go
+++ b/cmd/root_test.go
@@ -412,6 +412,13 @@ func TestNewCommandArguments(t *testing.T) {
 				MaxConnections: 1,
 			}),
 		},
+		{
+			desc: "using min-sigterm-delay flag",
+			args: []string{"--min-sigterm-delay", "10s", "projects/proj/locations/region/clusters/clust/instances/inst"},
+			want: withDefaults(&proxy.Config{
+				WaitBeforeClose: 10 * time.Second,
+			}),
+		},
 		{
 			desc: "using wait after signterm flag",
 			args: []string{"--max-sigterm-delay", "10s", "projects/proj/locations/region/clusters/clust/instances/inst"},
diff --git a/internal/proxy/proxy.go b/internal/proxy/proxy.go
index c1e3f56f..877532b0 100644
--- a/internal/proxy/proxy.go
+++ b/internal/proxy/proxy.go
@@ -142,6 +142,11 @@ type Config struct {
 	// connections. A zero-value indicates no limit.
 	MaxConnections uint64
 
+	// WaitBeforeClose sets the duration to wait after receiving a shutdown signal
+	// but before closing the process. Not setting this field means to initiate
+	// the shutdown process immediately.
+	WaitBeforeClose time.Duration
+
 	// WaitOnClose sets the duration to wait for connections to close before
 	// shutting down. Not setting this field means to close immediately
 	// regardless of any open connections.