diff --git a/bootstrap/bootstrap.go b/bootstrap/bootstrap.go
index 37ffdc25..221fde8b 100644
--- a/bootstrap/bootstrap.go
+++ b/bootstrap/bootstrap.go
@@ -72,6 +72,28 @@ type Bootstrap struct {
 	routes []route
 }
 
+// maxRequestsHandler bounds how many requests h serves at once. Requests
+// arriving while the limit is reached are answered with 503 rather than
+// queued, so that a scrape which cannot be served fails quickly instead of
+// piling up behind the ones that are already running.
+//
+// A limit of zero or less disables the bound and h is returned unchanged.
+func maxRequestsHandler(h http.Handler, limit int) http.Handler {
+	if limit <= 0 {
+		return h
+	}
+	inFlight := make(chan struct{}, limit)
+	return http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
+		select {
+		case inFlight <- struct{}{}:
+			defer func() { <-inFlight }()
+			h.ServeHTTP(w, r)
+		default:
+			http.Error(w, fmt.Sprintf("Limit of concurrent requests reached (%d), try again later.", limit), http.StatusServiceUnavailable)
+		}
+	})
+}
+
 // route is an additional handler registered next to the metrics endpoint.
 type route struct {
 	pattern string
@@ -172,11 +194,11 @@ func New(c Config) *Runner {
 		).Default("/metrics").String(),
 		disableExporterMetrics: app.Flag(
 			"web.disable-exporter-metrics",
-			"Exclude metrics about the exporter itself (promhttp_*, process_*, go_*).",
+			"Exclude metrics about the exporter itself (promhttp_*, process_*, go_*). Applied by the exporter's metrics handler, which is the only thing that knows what it collects; it is reported to a MetricsHandlerFactory as Bootstrap.DisableExporterMetrics.",
 		).Bool(),
 		maxRequests: app.Flag(
 			"web.max-requests",
-			"Maximum number of parallel scrape requests. Use 0 to disable.",
+			"Maximum number of scrape requests served in parallel. Further requests are answered with 503 until one completes. Use 0 to disable.",
 		).Default("40").Int(),
 	}
 
@@ -269,7 +291,7 @@ func (t *Runner) resolveMetricsHandler() (http.Handler, error) {
 func (t *Runner) newServer(metricsHandler http.Handler) (*http.Server, error) {
 	mux := http.NewServeMux()
 	metricsPath := t.MetricsPath
-	mux.Handle(metricsPath, metricsHandler)
+	mux.Handle(metricsPath, maxRequestsHandler(metricsHandler, t.MaxRequests))
 
 	rootOverridden := false
 	if t.bootstrap != nil {
diff --git a/bootstrap/max_requests_test.go b/bootstrap/max_requests_test.go
new file mode 100644
index 00000000..fefdfe34
--- /dev/null
+++ b/bootstrap/max_requests_test.go
@@ -0,0 +1,172 @@
+// Copyright The Prometheus Authors
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package bootstrap
+
+import (
+	"net/http"
+	"net/http/httptest"
+	"sync"
+	"testing"
+
+	"github.com/alecthomas/kingpin/v2"
+)
+
+// blockingHandler serves requests that block until release is closed, so that a
+// test can hold a known number of them in flight at once.
+type blockingHandler struct {
+	entered chan struct{}
+	release chan struct{}
+}
+
+func newBlockingHandler(capacity int) *blockingHandler {
+	return &blockingHandler{
+		entered: make(chan struct{}, capacity),
+		release: make(chan struct{}),
+	}
+}
+
+func (h *blockingHandler) ServeHTTP(w http.ResponseWriter, _ *http.Request) {
+	h.entered <- struct{}{}
+	<-h.release
+	w.Write([]byte("metrics"))
+}
+
+// runnerForMaxRequests builds a server whose metrics path is served by handler,
+// with --web.max-requests set to the given value.
+func runnerForMaxRequests(t *testing.T, handler http.Handler, args ...string) *http.Server {
+	t.Helper()
+	tk := New(Config{
+		App:            kingpin.New("test", ""),
+		Name:           "test_exporter",
+		DefaultAddress: ":0",
+		MetricsHandler: handler,
+	})
+	if err := tk.parse(args); err != nil {
+		t.Fatalf("parse: %v", err)
+	}
+	metricsHandler, err := tk.resolveMetricsHandler()
+	if err != nil {
+		t.Fatalf("resolveMetricsHandler: %v", err)
+	}
+	server, err := tk.newServer(metricsHandler)
+	if err != nil {
+		t.Fatalf("newServer: %v", err)
+	}
+	return server
+}
+
+// TestMaxRequestsLimitsParallelScrapes checks that --web.max-requests bounds
+// the number of scrapes served at once and answers the rest with 503.
+func TestMaxRequestsLimitsParallelScrapes(t *testing.T) {
+	handler := newBlockingHandler(2)
+	server := runnerForMaxRequests(t, handler, "--web.max-requests=1")
+
+	// Occupy the single slot and wait until the handler is actually running.
+	var wg sync.WaitGroup
+	wg.Go(func() {
+		rec := httptest.NewRecorder()
+		server.Handler.ServeHTTP(rec, httptest.NewRequest(http.MethodGet, "/metrics", nil))
+		if rec.Code != http.StatusOK {
+			t.Errorf("first request: got status %d, expected %d", rec.Code, http.StatusOK)
+		}
+	})
+	<-handler.entered
+
+	rec := httptest.NewRecorder()
+	server.Handler.ServeHTTP(rec, httptest.NewRequest(http.MethodGet, "/metrics", nil))
+	if rec.Code != http.StatusServiceUnavailable {
+		t.Errorf("second request: got status %d, expected %d", rec.Code, http.StatusServiceUnavailable)
+	}
+
+	close(handler.release)
+	wg.Wait()
+
+	// With the slot free again, a scrape is served.
+	handler2 := newBlockingHandler(1)
+	close(handler2.release)
+	server2 := runnerForMaxRequests(t, handler2, "--web.max-requests=1")
+	rec = httptest.NewRecorder()
+	server2.Handler.ServeHTTP(rec, httptest.NewRequest(http.MethodGet, "/metrics", nil))
+	if rec.Code != http.StatusOK {
+		t.Errorf("request after release: got status %d, expected %d", rec.Code, http.StatusOK)
+	}
+}
+
+// TestMaxRequestsZeroDisablesTheLimit checks that 0 means unlimited, as the
+// flag help says.
+func TestMaxRequestsZeroDisablesTheLimit(t *testing.T) {
+	handler := newBlockingHandler(4)
+	server := runnerForMaxRequests(t, handler, "--web.max-requests=0")
+
+	const parallel = 3
+	var wg sync.WaitGroup
+	for range parallel {
+		wg.Go(func() {
+			rec := httptest.NewRecorder()
+			server.Handler.ServeHTTP(rec, httptest.NewRequest(http.MethodGet, "/metrics", nil))
+			if rec.Code != http.StatusOK {
+				t.Errorf("got status %d, expected %d", rec.Code, http.StatusOK)
+			}
+		})
+	}
+	// All of them must get into the handler at the same time.
+	for range parallel {
+		<-handler.entered
+	}
+	close(handler.release)
+	wg.Wait()
+}
+
+// TestMaxRequestsDoesNotLimitOtherRoutes checks that the bound applies to the
+// metrics endpoint only, since that is what the flag describes.
+func TestMaxRequestsDoesNotLimitOtherRoutes(t *testing.T) {
+	metrics := newBlockingHandler(1)
+	tk := New(Config{
+		App:            kingpin.New("test", ""),
+		Name:           "test_exporter",
+		DefaultAddress: ":0",
+		MetricsHandlerFactory: func(b *Bootstrap) (http.Handler, error) {
+			b.HandleFunc("/healthz", func(w http.ResponseWriter, _ *http.Request) {
+				w.Write([]byte("ok"))
+			})
+			return metrics, nil
+		},
+	})
+	if err := tk.parse([]string{"--web.max-requests=1"}); err != nil {
+		t.Fatalf("parse: %v", err)
+	}
+	handler, err := tk.resolveMetricsHandler()
+	if err != nil {
+		t.Fatalf("resolveMetricsHandler: %v", err)
+	}
+	server, err := tk.newServer(handler)
+	if err != nil {
+		t.Fatalf("newServer: %v", err)
+	}
+
+	var wg sync.WaitGroup
+	wg.Go(func() {
+		server.Handler.ServeHTTP(httptest.NewRecorder(), httptest.NewRequest(http.MethodGet, "/metrics", nil))
+	})
+	<-metrics.entered
+
+	rec := httptest.NewRecorder()
+	server.Handler.ServeHTTP(rec, httptest.NewRequest(http.MethodGet, "/healthz", nil))
+	if rec.Code != http.StatusOK {
+		t.Errorf("/healthz while /metrics is saturated: got status %d, expected %d", rec.Code, http.StatusOK)
+	}
+
+	close(metrics.release)
+	wg.Wait()
+}