diff --git a/README.md b/README.md
index 85155a9..f07e4cc 100644
--- a/README.md
+++ b/README.md
@@ -168,8 +168,10 @@ either.
 - Request bodies for `POST /api/v1/session`, `POST /api/v1/login` and
   `POST /api/v1/messages` are limited to `MAX_MESSAGE_SIZE` bytes (default
   `4096`). A larger body gets `400` `invalid request body`.
-- The server allows cross-origin requests from any origin, with credentials. The
-  cookie is `SameSite=Strict`, so a browser sends it only from the same site.
+- A response to a cross-origin request carries `Access-Control-Allow-Origin: *`,
+  never the request's origin, and never `Access-Control-Allow-Credentials`. A
+  page on another origin therefore cannot read the response to a request that
+  carries the cookie.
 
 ### The auth cookie
 
@@ -1896,10 +1898,10 @@ The IRC listener has no TLS.
   carries a `Content-Security-Policy` header:
   `default-src 'self'; script-src 'self'; style-src 'self'; connect-src 'self'; img-src 'self'; font-src 'self'; object-src 'none'; frame-ancestors 'none'; base-uri 'self'; form-action 'self'`.
   The web client works within it.
-- Cross-origin requests are allowed from any origin, with credentials. The
-  allowed methods are `GET`, `POST`, `PUT`, `DELETE` and `OPTIONS`. The allowed
-  request headers are `Accept`, `Content-Type` and `X-CSRF-Token`. The cookie's
-  `SameSite=Strict` still keeps it to the same site.
+- A response to a cross-origin request carries `Access-Control-Allow-Origin: *`,
+  never the request's origin, and never `Access-Control-Allow-Credentials`. A
+  page on another origin therefore cannot read the response to a request that
+  carries the cookie.
 
 ### Logging
 
diff --git a/internal/middleware/middleware.go b/internal/middleware/middleware.go
index 52469ef..59b47af 100644
--- a/internal/middleware/middleware.go
+++ b/internal/middleware/middleware.go
@@ -201,23 +201,19 @@ func (mware *Middleware) Logging() func(http.Handler) http.Handler {
 }
 
 // CORS returns middleware that handles Cross-Origin Resource Sharing.
-// AllowCredentials is true so browsers include cookies in
-// cross-origin API requests.
+// It allows every origin, without credentials, so a page on another
+// origin cannot read what the signed-in user sees.
 func (mware *Middleware) CORS() func(http.Handler) http.Handler {
 	return cors.Handler(cors.Options{ //nolint:exhaustruct // optional fields
-		AllowOriginFunc: func(
-			_ *http.Request, _ string,
-		) bool {
-			return true
-		},
+		AllowedOrigins: []string{"*"},
 		AllowedMethods: []string{
 			"GET", "POST", "PUT", "DELETE", "OPTIONS",
 		},
 		AllowedHeaders: []string{
-			"Accept", "Content-Type", "X-CSRF-Token",
+			"Accept", "Authorization", "Content-Type", "X-CSRF-Token",
 		},
 		ExposedHeaders:   []string{"Link"},
-		AllowCredentials: true,
+		AllowCredentials: false,
 		MaxAge:           corsMaxAge,
 	})
 }
diff --git a/internal/server/server_test.go b/internal/server/server_test.go
index 6a44326..3e88589 100644
--- a/internal/server/server_test.go
+++ b/internal/server/server_test.go
@@ -8,6 +8,7 @@ import (
 	"fmt"
 	"net"
 	"net/http"
+	"net/http/httptest"
 	"strconv"
 	"strings"
 	"testing"
@@ -188,6 +189,62 @@ func TestServeAfterStopDoesNotStopApp(t *testing.T) {
 	}
 }
 
+// TestCORSAllowsAnyOriginWithoutCredentials checks that the
+// responses to a request from another origin and to a preflight
+// both carry Access-Control-Allow-Origin: *, never the request's
+// origin, and no Access-Control-Allow-Credentials.
+func TestCORSAllowsAnyOriginWithoutCredentials(t *testing.T) {
+	var srv *server.Server
+
+	startApp(t, fx.Populate(&srv))
+
+	tests := []struct {
+		name          string
+		method        string
+		requestMethod string
+	}{
+		{
+			name:   "request",
+			method: http.MethodGet,
+		},
+		{
+			name:          "preflight",
+			method:        http.MethodOptions,
+			requestMethod: http.MethodPost,
+		},
+	}
+
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			request := httptest.NewRequestWithContext(
+				t.Context(), test.method,
+				"http://chat.example.com/api/v1/server", nil,
+			)
+			request.Header.Set("Origin", "http://blog.example.com")
+
+			if test.requestMethod != "" {
+				request.Header.Set(
+					"Access-Control-Request-Method", test.requestMethod,
+				)
+			}
+
+			recorder := httptest.NewRecorder()
+
+			srv.ServeHTTP(recorder, request)
+
+			for header, want := range map[string]string{
+				"Access-Control-Allow-Origin":      "*",
+				"Access-Control-Allow-Credentials": "",
+			} {
+				got := recorder.Header().Get(header)
+				if got != want {
+					t.Errorf("%s is %q, want %q", header, got, want)
+				}
+			}
+		})
+	}
+}
+
 // startApp starts the app newApp builds, with the HTTP port
 // set to 0, so the system gives the server a free port.
 func startApp(