diff --git a/modules/caddyhttp/app.go b/modules/caddyhttp/app.go
index 429e8ebdc6f..a01f9ee4b92 100644
--- a/modules/caddyhttp/app.go
+++ b/modules/caddyhttp/app.go
@@ -18,7 +18,6 @@ import (
 	"context"
 	"crypto/tls"
 	"fmt"
-	"net"
 	"net/http"
 	"strconv"
 	"sync"
@@ -364,7 +363,11 @@ func (app *App) Start() error {
 			h2server := &http2.Server{
 				NewWriteScheduler: func() http2.WriteScheduler { return http2.NewPriorityWriteScheduler(nil) },
 			}
-			srv.server.Handler = h2c.NewHandler(srv, h2server)
+			//nolint:errcheck
+			http2.ConfigureServer(srv.server, h2server)
+			h2chandler := newH2cHandler(h2c.NewHandler(srv, h2server))
+			srv.server.Handler = h2chandler
+			srv.h2chandler = h2chandler
 		}
 
 		for _, lnAddr := range srv.Listen {
@@ -502,14 +505,6 @@ func (app *App) Stop() error {
 				zap.Error(err),
 				zap.Strings("addresses", server.Listen))
 		}
-	}
-	for i, s := range app.h2chandlers {
-		if err := s.Shutdown(ctx); err != nil {
-			app.logger.Error("h2c handler shutdown",
-				zap.Error(err),
-				zap.Int("index", i))
-		}
-	}
 
 		if server.h3server != nil {
 			// TODO: CloseGracefully, once implemented upstream (see https://github.com/lucas-clemente/quic-go/issues/2103)
@@ -519,6 +514,14 @@ func (app *App) Stop() error {
 					zap.Strings("addresses", server.Listen))
 			}
 		}
+
+		if server.h2chandler != nil {
+			if err := server.h2chandler.Shutdown(ctx); err != nil {
+				app.logger.Error("h2c handler shutdown",
+					zap.Error(err),
+					zap.Strings("addresses", server.Listen))
+			}
+		}
 	}
 
 	return nil
diff --git a/modules/caddyhttp/h2chandler/handler.go b/modules/caddyhttp/h2chandler.go
similarity index 81%
rename from modules/caddyhttp/h2chandler/handler.go
rename to modules/caddyhttp/h2chandler.go
index 6b709fa00c1..7d638fc4bca 100644
--- a/modules/caddyhttp/h2chandler/handler.go
+++ b/modules/caddyhttp/h2chandler.go
@@ -1,4 +1,4 @@
-package h2chandler
+package caddyhttp
 
 import (
 	"context"
@@ -11,15 +11,15 @@ import (
 	"golang.org/x/net/http/httpguts"
 )
 
-// Handler is a Handler which counts possible h2c upgrade requests
-type Handler struct {
+// h2chandler is a Handler which counts possible h2c upgrade requests
+type h2chandler struct {
 	cnt     uint64
 	Handler http.Handler
 }
 
-// NewHandler returns an http.Handler that tracks possible h2c upgrade requests.
-func NewHandler(h http.Handler) *Handler {
-	return &Handler{
+// NewH2cHandler returns an http.Handler that tracks possible h2c upgrade requests.
+func newH2cHandler(h http.Handler) *h2chandler {
+	return &h2chandler{
 		Handler: h,
 	}
 }
@@ -27,7 +27,7 @@ func NewHandler(h http.Handler) *Handler {
 const shutdownPollIntervalMax = 500 * time.Millisecond
 
 // Shutdown mirrors stdlib http.Server Shutdown behavior, because h2 connections are always marked active, there is no closing to be done.
-func (h *Handler) Shutdown(ctx context.Context) error {
+func (h *h2chandler) Shutdown(ctx context.Context) error {
 	pollIntervalBase := time.Millisecond
 	nextPollInterval := func() time.Duration {
 		// Add 10% jitter.
@@ -70,7 +70,7 @@ func isH2cUpgrade(r *http.Request) bool {
 }
 
 // ServeHTTP records underlying connections that are likely to be h2c.
-func (h *Handler) ServeHTTP(w http.ResponseWriter, r *http.Request) {
+func (h *h2chandler) ServeHTTP(w http.ResponseWriter, r *http.Request) {
 	if isH2cUpgrade(r) {
 		atomic.AddUint64(&h.cnt, 1)
 		defer atomic.AddUint64(&h.cnt, ^uint64(0))
diff --git a/modules/caddyhttp/server.go b/modules/caddyhttp/server.go
index f8cd612278a..5c783d51e10 100644
--- a/modules/caddyhttp/server.go
+++ b/modules/caddyhttp/server.go
@@ -162,6 +162,8 @@ type Server struct {
 	h3server  *http3.Server
 	addresses []caddy.NetworkAddress
 
+	h2chandler *h2chandler
+
 	shutdownAt   time.Time
 	shutdownAtMu *sync.RWMutex
 }