diff --git a/internal/jsonrpc2/conn.go b/internal/jsonrpc2/conn.go
index bc85191..0741696 100644
--- a/internal/jsonrpc2/conn.go
+++ b/internal/jsonrpc2/conn.go
@@ -27,14 +27,16 @@ import (
 type Binder interface {
 	// Bind returns the ConnectionOptions to use when establishing the passed-in
 	// Connection.
-	// The connection is not ready to use when Bind is called.
-	Bind(context.Context, *Connection) (ConnectionOptions, error)
+	//
+	// The connection is not ready to use when Bind is called,
+	// but Bind may close it without reading or writing to it.
+	Bind(context.Context, *Connection) ConnectionOptions
 }
 
 // A BinderFunc implements the Binder interface for a standalone Bind function.
-type BinderFunc func(context.Context, *Connection) (ConnectionOptions, error)
+type BinderFunc func(context.Context, *Connection) ConnectionOptions
 
-func (f BinderFunc) Bind(ctx context.Context, c *Connection) (ConnectionOptions, error) {
+func (f BinderFunc) Bind(ctx context.Context, c *Connection) ConnectionOptions {
 	return f(ctx, c)
 }
 
@@ -130,8 +132,8 @@ type incomingRequest struct {
 }
 
 // Bind returns the options unmodified.
-func (o ConnectionOptions) Bind(context.Context, *Connection) (ConnectionOptions, error) {
-	return o, nil
+func (o ConnectionOptions) Bind(context.Context, *Connection) ConnectionOptions {
+	return o
 }
 
 // newConnection creates a new connection and runs it.
@@ -141,7 +143,7 @@ func (o ConnectionOptions) Bind(context.Context, *Connection) (ConnectionOptions
 // The connection is closed automatically (and its resources cleaned up) when
 // the last request has completed after the underlying ReadWriteCloser breaks,
 // but it may be stopped earlier by calling Close (for a clean shutdown).
-func newConnection(bindCtx context.Context, rwc io.ReadWriteCloser, binder Binder, onDone func()) (*Connection, error) {
+func newConnection(bindCtx context.Context, rwc io.ReadWriteCloser, binder Binder, onDone func()) *Connection {
 	// TODO: Should we create a new event span here?
 	// This will propagate cancellation from ctx; should it?
 	ctx := notDone{bindCtx}
@@ -153,10 +155,7 @@ func newConnection(bindCtx context.Context, rwc io.ReadWriteCloser, binder Binde
 		onDone:   onDone,
 	}
 
-	options, err := binder.Bind(bindCtx, c)
-	if err != nil {
-		return nil, err
-	}
+	options := binder.Bind(bindCtx, c)
 	framer := options.Framer
 	if framer == nil {
 		framer = HeaderFramer()
@@ -169,9 +168,14 @@ func newConnection(bindCtx context.Context, rwc io.ReadWriteCloser, binder Binde
 
 	c.writer <- framer.Writer(rwc)
 	reader := framer.Reader(rwc)
-	// The goroutines started here will continue until the underlying stream is closed.
-	go c.readIncoming(ctx, reader, options.Preempter)
-	return c, nil
+
+	c.updateInFlight(func(s *inFlightState) {
+		if !s.closed {
+			// The goroutine started here will continue until the underlying stream is closed.
+			go c.readIncoming(ctx, reader, options.Preempter)
+		}
+	})
+	return c
 }
 
 // Notify invokes the target method but does not wait for a response.
diff --git a/internal/jsonrpc2/jsonrpc2_test.go b/internal/jsonrpc2/jsonrpc2_test.go
index 64aff2e..5357982 100644
--- a/internal/jsonrpc2/jsonrpc2_test.go
+++ b/internal/jsonrpc2/jsonrpc2_test.go
@@ -253,7 +253,7 @@ func verifyResults(t *testing.T, method string, results interface{}, expect inte
 	}
 }
 
-func (b binder) Bind(ctx context.Context, conn *jsonrpc2.Connection) (jsonrpc2.ConnectionOptions, error) {
+func (b binder) Bind(ctx context.Context, conn *jsonrpc2.Connection) jsonrpc2.ConnectionOptions {
 	h := &handler{
 		conn:    conn,
 		waiters: make(chan map[string]chan struct{}, 1),
@@ -267,7 +267,7 @@ func (b binder) Bind(ctx context.Context, conn *jsonrpc2.Connection) (jsonrpc2.C
 		Framer:    b.framer,
 		Preempter: h,
 		Handler:   h,
-	}, nil
+	}
 }
 
 func (h *handler) waiter(name string) chan struct{} {
diff --git a/internal/jsonrpc2/serve.go b/internal/jsonrpc2/serve.go
index d24e243..94e90b4 100644
--- a/internal/jsonrpc2/serve.go
+++ b/internal/jsonrpc2/serve.go
@@ -60,12 +60,7 @@ func Dial(ctx context.Context, dialer Dialer, binder Binder) (*Connection, error
 	if err != nil {
 		return nil, err
 	}
-	conn, err := newConnection(ctx, rwc, binder, nil)
-	if err != nil {
-		rwc.Close()
-		return nil, err
-	}
-	return conn, nil
+	return newConnection(ctx, rwc, binder, nil), nil
 }
 
 // Serve starts a new server listening for incoming connections and returns
@@ -120,12 +115,7 @@ func (s *Server) run(ctx context.Context) {
 
 		// A new inbound connection.
 		activeConns.Add(1)
-		_, err = newConnection(ctx, rwc, s.binder, activeConns.Done) // unregisters itself when done
-		if err != nil {
-			rwc.Close()
-			activeConns.Done()
-			s.async.setError(err)
-		}
+		_ = newConnection(ctx, rwc, s.binder, activeConns.Done) // unregisters itself when done
 	}
 	activeConns.Wait()
 }
diff --git a/internal/jsonrpc2/serve_test.go b/internal/jsonrpc2/serve_test.go
index 64985d7..5bb4aab 100644
--- a/internal/jsonrpc2/serve_test.go
+++ b/internal/jsonrpc2/serve_test.go
@@ -288,7 +288,7 @@ func TestCloseCallRace(t *testing.T) {
 
 		pokec := make(chan *jsonrpc2.AsyncCall, 1)
 
-		s, err := jsonrpc2.Serve(ctx, listener, jsonrpc2.BinderFunc(func(_ context.Context, srvConn *jsonrpc2.Connection) (jsonrpc2.ConnectionOptions, error) {
+		s, err := jsonrpc2.Serve(ctx, listener, jsonrpc2.BinderFunc(func(_ context.Context, srvConn *jsonrpc2.Connection) jsonrpc2.ConnectionOptions {
 			h := jsonrpc2.HandlerFunc(func(ctx context.Context, _ *jsonrpc2.Request) (interface{}, error) {
 				// Start a concurrent call from the server to the client.
 				// The point of this test is to ensure this doesn't deadlock
@@ -303,7 +303,7 @@ func TestCloseCallRace(t *testing.T) {
 
 				return &msg{"pong"}, nil
 			})
-			return jsonrpc2.ConnectionOptions{Handler: h}, nil
+			return jsonrpc2.ConnectionOptions{Handler: h}
 		}))
 		if err != nil {
 			listener.Close()