diff --git a/Dockerfile b/Dockerfile
index ca8536b..8fc074c 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -56,8 +56,9 @@ VOLUME /app/config
 RUN mkdir -p /app/data
 VOLUME /app/data
 
-# Healthy when the server answers and can reach its database
-HEALTHCHECK --interval=30s --timeout=5s --start-period=30s --start-interval=2s --retries=3 \
+# Healthy when the server answers and can reach its database.
+# (No --start-interval: it needs Docker 25, and deploy/rezervator.sh probes on its own.)
+HEALTHCHECK --interval=30s --timeout=5s --start-period=30s --retries=3 \
   CMD ["/app/rezervator", "-c", "/app/config/config.toml", "--healthcheck"]
 
 # Run the server
diff --git a/deploy/README.md b/deploy/README.md
index 1d11c1a..868aa99 100644
--- a/deploy/README.md
+++ b/deploy/README.md
@@ -20,7 +20,7 @@ The two settings are independent. [Setup with nginx and PostgreSQL on the host](
 
 ## Requirements
 
-- Docker with the Compose plugin, `bash` and `openssl` on the host
+- Docker 20.10 or newer, `bash` and `openssl` on the host. The Compose plugin is needed only when Traefik or PostgreSQL run as containers of this stack.
 - The application image on the host: `docker build -t rezervator:latest .` in the repository root, or pulled from a registry. The image must match the CPU architecture of the host.
 - A DNS record for every customer domain pointing to the host
 
diff --git a/deploy/rezervator.sh b/deploy/rezervator.sh
index 8369e43..330e804 100755
--- a/deploy/rezervator.sh
+++ b/deploy/rezervator.sh
@@ -267,28 +267,55 @@ run_container() {
     docker run "${args[@]}" "$image" >/dev/null
 }
 
-# Waits until the container reports healthy. Returns 1 when it stops or stays unhealthy.
+# Waits until the application in the container is up and can reach its database.
+# Returns 1 when the container stops or does not get healthy in time.
 wait_healthy() {
-    local container="$1" status
-    for _ in $(seq 1 90); do
-        status="$(docker inspect --format '{{.State.Status}} {{if .State.Health}}{{.State.Health.Status}}{{else}}none{{end}}' "$container" 2>/dev/null || echo "missing")"
-        case "$status" in
-            "running healthy")
-                # Traefik picks a new container up a moment after it turns healthy
-                if [ "$PROXY" = "traefik" ]; then sleep 3; fi
-                return 0 ;;
-            # Image without a health check: running for a while is the best we can tell
-            "running none") sleep 5
-                [ "$(docker inspect --format '{{.State.Status}}' "$container" 2>/dev/null)" = "running" ] && return 0
-                return 1 ;;
-            "running starting") ;;
-            "running unhealthy") return 1 ;;
-            running*) ;;
+    local container="$1" state has_check
+    has_check="$(docker inspect --format '{{if .Config.Healthcheck}}yes{{else}}no{{end}}' "$container" 2>/dev/null || echo "no")"
+
+    if [ "$has_check" = "no" ]; then
+        # Image from before the health check: running for a while is the best we can tell
+        sleep 5
+        [ "$(docker inspect --format '{{.State.Status}}' "$container" 2>/dev/null)" = "running" ]
+        return
+    fi
+
+    # Probe directly instead of waiting for Docker: its first check comes only after the
+    # check interval, and the faster start interval needs Docker 25
+    local ready="no"
+    for _ in $(seq 1 60); do
+        state="$(docker inspect --format '{{.State.Status}}' "$container" 2>/dev/null || echo "missing")"
+        case "$state" in
+            running)
+                if docker exec "$container" /app/rezervator -c /app/config/config.toml --healthcheck >/dev/null 2>&1; then
+                    ready="yes"
+                    break
+                fi ;;
+            restarting|created) ;;
             *) return 1 ;;
         esac
+        # A container that fails at start is restarted by Docker over and over
+        if [ "$(docker inspect --format '{{.RestartCount}}' "$container" 2>/dev/null || echo 0)" -ge 3 ]; then
+            return 1
+        fi
         sleep 2
     done
-    return 1
+    [ "$ready" = "yes" ] || return 1
+
+    if [ "$PROXY" = "traefik" ]; then
+        # Traefik routes to the container only once Docker itself reports it healthy
+        for _ in $(seq 1 45); do
+            state="$(docker inspect --format '{{.State.Health.Status}}' "$container" 2>/dev/null || echo "missing")"
+            case "$state" in
+                healthy) sleep 3; return 0 ;;
+                starting) ;;
+                *) return 1 ;;
+            esac
+            sleep 2
+        done
+        return 1
+    fi
+    return 0
 }
 
 cmd_init() {