diff --git a/pgconn/config.go b/pgconn/config.go
index d2001dc5..a07fa533 100644
--- a/pgconn/config.go
+++ b/pgconn/config.go
@@ -20,6 +20,8 @@ import (
 	"github.com/pkg/errors"
 )
 
+type AcceptConnFunc func(pgconn *PgConn) bool
+
 // Config is the settings used to establish a connection to a PostgreSQL server.
 type Config struct {
 	Host          string // host (e.g. localhost) or path to unix domain socket directory (e.g. /private/tmp)
@@ -32,6 +34,11 @@ type Config struct {
 	RuntimeParams map[string]string // Run-time parameters to set on connection as session default values (e.g. search_path or application_name)
 
 	Fallbacks []*FallbackConfig
+
+	// AcceptConnFunc is called after successful connection allow custom logic for determining if the connection is
+	// acceptable. If AcceptConnFunc returns false the connection is closed and the next fallback config is tried. This
+	// allows implementing high availability behavior such as libpq does with target_session_attrs.
+	AcceptConnFunc AcceptConnFunc
 }
 
 // FallbackConfig is additional settings to attempt a connection with when the primary Config fails to establish a
diff --git a/pgconn/pgconn.go b/pgconn/pgconn.go
index 09860eb2..ac48f870 100644
--- a/pgconn/pgconn.go
+++ b/pgconn/pgconn.go
@@ -137,6 +137,7 @@ func connect(ctx context.Context, config *Config, fallbackConfig *FallbackConfig
 
 	if config.TLSConfig != nil {
 		if err := pgConn.startTLS(config.TLSConfig); err != nil {
+			pgConn.NetConn.Close()
 			return nil, err
 		}
 	}
@@ -162,6 +163,7 @@ func connect(ctx context.Context, config *Config, fallbackConfig *FallbackConfig
 	}
 
 	if _, err := pgConn.NetConn.Write(startupMsg.Encode(nil)); err != nil {
+		pgConn.NetConn.Close()
 		return nil, err
 	}
 
@@ -177,13 +179,19 @@ func connect(ctx context.Context, config *Config, fallbackConfig *FallbackConfig
 			pgConn.SecretKey = msg.SecretKey
 		case *pgproto3.Authentication:
 			if err = pgConn.rxAuthenticationX(msg); err != nil {
+				pgConn.NetConn.Close()
 				return nil, err
 			}
 		case *pgproto3.ReadyForQuery:
-			return pgConn, nil
+			if config.AcceptConnFunc == nil || config.AcceptConnFunc(pgConn) {
+				return pgConn, nil
+			}
+			pgConn.NetConn.Close()
+			return nil, errors.New("AcceptConnFunc rejected connection")
 		case *pgproto3.ParameterStatus:
 			// handled by ReceiveMessage
 		case *pgproto3.ErrorResponse:
+			pgConn.NetConn.Close()
 			return nil, PgError{
 				Severity:         msg.Severity,
 				Code:             msg.Code,
@@ -204,6 +212,7 @@ func connect(ctx context.Context, config *Config, fallbackConfig *FallbackConfig
 				Routine:          msg.Routine,
 			}
 		default:
+			pgConn.NetConn.Close()
 			return nil, errors.New("unexpected message")
 		}
 	}
diff --git a/pgconn/pgconn_test.go b/pgconn/pgconn_test.go
index d53bbc09..ad06ae7b 100644
--- a/pgconn/pgconn_test.go
+++ b/pgconn/pgconn_test.go
@@ -188,6 +188,40 @@ func TestConnectWithFallback(t *testing.T) {
 	closeConn(t, conn)
 }
 
+func TestConnectWithAcceptConnFunc(t *testing.T) {
+	config, err := pgconn.ParseConfig(os.Getenv("PGX_TEST_DATABASE"))
+	require.Nil(t, err)
+
+	dialCount := 0
+	config.DialFunc = func(ctx context.Context, network, address string) (net.Conn, error) {
+		dialCount += 1
+		return net.Dial(network, address)
+	}
+
+	acceptConnCount := 0
+	config.AcceptConnFunc = func(conn *pgconn.PgConn) bool {
+		acceptConnCount += 1
+		return acceptConnCount > 1
+	}
+
+	// Append current primary config to fallbacks
+	config.Fallbacks = append(config.Fallbacks, &pgconn.FallbackConfig{
+		Host:      config.Host,
+		Port:      config.Port,
+		TLSConfig: config.TLSConfig,
+	})
+
+	// Repeat fallbacks
+	config.Fallbacks = append(config.Fallbacks, config.Fallbacks...)
+
+	conn, err := pgconn.ConnectConfig(context.Background(), config)
+	require.Nil(t, err)
+	closeConn(t, conn)
+
+	assert.True(t, dialCount > 1)
+	assert.True(t, acceptConnCount > 1)
+}
+
 func TestSimple(t *testing.T) {
 	pgConn, err := pgconn.Connect(context.Background(), os.Getenv("PGX_TEST_DATABASE"))
 	require.Nil(t, err)