diff --git a/http2/server.go b/http2/server.go
index d4abeb2b..57334dc7 100644
--- a/http2/server.go
+++ b/http2/server.go
@@ -273,7 +273,20 @@ func ConfigureServer(s *http.Server, conf *Server) error {
 		if testHookOnConn != nil {
 			testHookOnConn()
 		}
+		// The TLSNextProto interface predates contexts, so
+		// the net/http package passes down its per-connection
+		// base context via an exported but unadvertised
+		// method on the Handler. This is for internal
+		// net/http<=>http2 use only.
+		var ctx context.Context
+		type baseContexter interface {
+			BaseContext() context.Context
+		}
+		if bc, ok := h.(baseContexter); ok {
+			ctx = bc.BaseContext()
+		}
 		conf.ServeConn(c, &ServeConnOpts{
+			Context:    ctx,
 			Handler:    h,
 			BaseConfig: hs,
 		})
@@ -284,6 +297,10 @@ func ConfigureServer(s *http.Server, conf *Server) error {
 
 // ServeConnOpts are options for the Server.ServeConn method.
 type ServeConnOpts struct {
+	// Context is the base context to use.
+	// If nil, context.Background is used.
+	Context context.Context
+
 	// BaseConfig optionally sets the base configuration
 	// for values. If nil, defaults are used.
 	BaseConfig *http.Server
@@ -294,6 +311,13 @@ type ServeConnOpts struct {
 	Handler http.Handler
 }
 
+func (o *ServeConnOpts) context() context.Context {
+	if o.Context != nil {
+		return o.Context
+	}
+	return context.Background()
+}
+
 func (o *ServeConnOpts) baseConfig() *http.Server {
 	if o != nil && o.BaseConfig != nil {
 		return o.BaseConfig
@@ -439,7 +463,7 @@ func (s *Server) ServeConn(c net.Conn, opts *ServeConnOpts) {
 }
 
 func serverConnBaseContext(c net.Conn, opts *ServeConnOpts) (ctx context.Context, cancel func()) {
-	ctx, cancel = context.WithCancel(context.Background())
+	ctx, cancel = context.WithCancel(opts.context())
 	ctx = context.WithValue(ctx, http.LocalAddrContextKey, c.LocalAddr())
 	if hs := opts.baseConfig(); hs != nil {
 		ctx = context.WithValue(ctx, http.ServerContextKey, hs)