diff --git a/internal/api/api.go b/internal/api/api.go
index 3fbd21c..fbbe9db 100644
--- a/internal/api/api.go
+++ b/internal/api/api.go
@@ -95,6 +95,9 @@ func New(p Params) *http.Server {
 		ReadTimeout:       readTimeout,
 		WriteTimeout:      writeTimeout,
 		IdleTimeout:       idleTimeout,
+		// Otherwise net/http answers "OPTIONS *" itself, with 200 and
+		// without the credential check or the headers.
+		DisableGeneralOptionsHandler: true,
 		// net/http's own messages, such as a handler's panic, go to the
 		// same JSON log as everything else.
 		ErrorLog: slog.NewLogLogger(p.Log.Handler(), slog.LevelError),
diff --git a/internal/api/api_test.go b/internal/api/api_test.go
index be3a2da..2f78fe4 100644
--- a/internal/api/api_test.go
+++ b/internal/api/api_test.go
@@ -4,7 +4,9 @@ import (
 	"bytes"
 	"context"
 	"errors"
+	"io"
 	"log/slog"
+	"net"
 	"net/http"
 	"net/http/httptest"
 	"strings"
@@ -175,6 +177,49 @@ func TestNoPathIsExempt(t *testing.T) {
 	}
 }
 
+// TestOptionsAsterisk: "OPTIONS *" is refused like any other request.
+// net/http would answer it before the handler, so this request goes to
+// a running server rather than to its handler.
+func TestOptionsAsterisk(t *testing.T) {
+	t.Parallel()
+
+	srv := newAPI("", &fakeClient{})
+
+	listener, err := (&net.ListenConfig{}).Listen(t.Context(), "tcp", "127.0.0.1:0")
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	go func() { _ = srv.Serve(listener) }()
+
+	t.Cleanup(func() { _ = srv.Close() })
+
+	req, err := http.NewRequestWithContext(t.Context(), http.MethodOptions,
+		"http://"+listener.Addr().String(), nil)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	// The request line becomes "OPTIONS * HTTP/1.1".
+	req.URL.Opaque = "*"
+
+	resp, err := http.DefaultClient.Do(req)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	defer func() { _ = resp.Body.Close() }()
+
+	body, err := io.ReadAll(resp.Body)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	if resp.StatusCode != http.StatusUnauthorized || string(body) != unauthorized {
+		t.Errorf("OPTIONS *: %d %q, want 401 %q", resp.StatusCode, body, unauthorized)
+	}
+}
+
 // TestHeaders: every response, whatever its status, carries the
 // security headers, and none lets another origin in.
 func TestHeaders(t *testing.T) {