diff --git a/internal/app/app_test.go b/internal/app/app_test.go
new file mode 100644
index 0000000..6c7321a
--- /dev/null
+++ b/internal/app/app_test.go
@@ -0,0 +1,164 @@
+package app_test
+
+import (
+	"bytes"
+	"errors"
+	"fmt"
+	"net"
+	"net/http"
+	"os"
+	"os/exec"
+	"strconv"
+	"syscall"
+	"testing"
+	"time"
+
+	"sneak.berlin/go/pixa/internal/app"
+)
+
+// These tests run pixad in a child process: the test binary itself,
+// started again with runPixadInChildEnvVar set, which makes TestMain run
+// pixad instead of the tests.
+const runPixadInChildEnvVar = "TEST_RUN_PIXAD_IN_CHILD"
+
+const validTestSigningKey = "test-signing-key-for-app-tests-0123456789"
+
+func TestMain(m *testing.M) {
+	if os.Getenv(runPixadInChildEnvVar) == "1" {
+		os.Args = []string{"pixad"}
+
+		app.Run("test")
+		os.Exit(0)
+	}
+
+	os.Exit(m.Run())
+}
+
+// pixadCommand returns a command that runs pixad with only the given
+// environment, in an empty directory with an empty HOME, so that no
+// config file is found.
+func pixadCommand(t *testing.T, env ...string) (*exec.Cmd, *bytes.Buffer) {
+	t.Helper()
+
+	testBinary := os.Args[0]
+	cmd := exec.CommandContext(t.Context(), testBinary) //nolint:gosec // not tainted
+	cmd.Dir = t.TempDir()
+	cmd.Env = append([]string{
+		runPixadInChildEnvVar + "=1",
+		"HOME=" + t.TempDir(),
+	}, env...)
+
+	var stderr bytes.Buffer
+
+	cmd.Stderr = &stderr
+
+	return cmd, &stderr
+}
+
+// TestRunPrintsStartupErrorOnce checks that an invalid setting is
+// printed once, as the line that names it, and nothing else goes to
+// stderr.
+func TestRunPrintsStartupErrorOnce(t *testing.T) {
+	t.Parallel()
+
+	cmd, stderr := pixadCommand(t, "PIXA_SIGNING_KEY=short")
+
+	err := cmd.Run()
+
+	var exitErr *exec.ExitError
+	if !errors.As(err, &exitErr) || exitErr.ExitCode() != 1 {
+		t.Fatalf("pixad: got %v, want exit status 1; stderr:\n%s", err, stderr)
+	}
+
+	want := `config key "signing_key" (environment variable PIXA_SIGNING_KEY): ` +
+		"value too short: must be at least 32 characters, got 5\n"
+	if stderr.String() != want {
+		t.Errorf("stderr:\n%s\nwant:\n%s", stderr, want)
+	}
+}
+
+// TestRunWritesNothingToStderrOnStartAndStop starts pixad, waits until
+// it answers its health check, stops it with SIGTERM, and checks that it
+// wrote nothing to stderr.
+func TestRunWritesNothingToStderrOnStartAndStop(t *testing.T) {
+	t.Parallel()
+
+	port := freePort(t)
+	cmd, stderr := pixadCommand(t,
+		"PORT="+strconv.Itoa(port),
+		"PIXA_STATE_DIR="+t.TempDir(),
+		"PIXA_SIGNING_KEY="+validTestSigningKey,
+	)
+
+	err := cmd.Start()
+	if err != nil {
+		t.Fatalf("starting pixad: %v", err)
+	}
+
+	waitForHealthCheck(t, port)
+
+	err = cmd.Process.Signal(syscall.SIGTERM)
+	if err != nil {
+		t.Fatalf("signalling pixad: %v", err)
+	}
+
+	err = cmd.Wait()
+	if err != nil {
+		t.Fatalf("pixad: got %v, want exit status 0; stderr:\n%s", err, stderr)
+	}
+
+	if stderr.Len() != 0 {
+		t.Errorf("stderr is not empty:\n%s", stderr)
+	}
+}
+
+// freePort returns a TCP port on the loopback address that nothing
+// listens on.
+func freePort(t *testing.T) int {
+	t.Helper()
+
+	var listenConfig net.ListenConfig
+
+	listener, err := listenConfig.Listen(t.Context(), "tcp", "127.0.0.1:0")
+	if err != nil {
+		t.Fatalf("finding a free port: %v", err)
+	}
+
+	port := listener.Addr().(*net.TCPAddr).Port //nolint:forcetypeassert // a TCP listener
+
+	err = listener.Close()
+	if err != nil {
+		t.Fatalf("closing listener: %v", err)
+	}
+
+	return port
+}
+
+// waitForHealthCheck waits up to 30 seconds for pixad to answer its
+// health check on port.
+func waitForHealthCheck(t *testing.T, port int) {
+	t.Helper()
+
+	url := fmt.Sprintf("http://127.0.0.1:%d/.well-known/healthcheck.json", port)
+	deadline := time.Now().Add(30 * time.Second)
+
+	for time.Now().Before(deadline) {
+		req, err := http.NewRequestWithContext(t.Context(), http.MethodGet, url, nil)
+		if err != nil {
+			t.Fatalf("health check request: %v", err)
+		}
+
+		resp, err := http.DefaultClient.Do(req)
+		if err == nil {
+			_ = resp.Body.Close()
+
+			if resp.StatusCode == http.StatusOK {
+				return
+			}
+		}
+
+		time.Sleep(100 * time.Millisecond)
+	}
+
+	t.Fatalf("pixad did not answer its health check on port %d", port)
+}