diff --git a/.github/workflows/publish.yml b/.github/workflows/publish.yml
index d3597f0..0c2543d 100644
--- a/.github/workflows/publish.yml
+++ b/.github/workflows/publish.yml
@@ -44,8 +44,12 @@ jobs:
             CREATE EXTENSION postgis_tiger_geocoder CASCADE;
             CREATE EXTENSION vector;
             CREATE EXTENSION pg_trgm;
+            CREATE EXTENSION hypopg;
+            CREATE EXTENSION pg_stat_statements;
             SELECT extname, extversion FROM pg_extension ORDER BY extname;
-            SELECT '[1,2,3]'::vector <=> '[1,2,4]'::vector AS cosine_distance, ST_AsText(ST_MakePoint(24.57, 59.34)) AS point;"
+            SELECT '[1,2,3]'::vector <=> '[1,2,4]'::vector AS cosine_distance, ST_AsText(ST_MakePoint(24.57, 59.34)) AS point;
+            SELECT indexname AS hypothetical_index FROM hypopg_create_index('CREATE INDEX ON pg_class (relname)');
+            SELECT count(*) > 0 AS statements_tracked FROM pg_stat_statements;"
       - uses: docker/metadata-action@v6
         id: meta
         with:
diff --git a/Dockerfile b/Dockerfile
index 251ff6e..075dddd 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -1,4 +1,4 @@
-# PostgreSQL 18 with PostGIS 3 and pgvector. The official postgres image is multi-architecture
+# PostgreSQL 18 with PostGIS 3, pgvector and hypopg. The official postgres image is multi-architecture
 # (x86 and Arm) and Debian-based, with the PostgreSQL project's apt repository configured, whose
 # extension packages follow each release.
 FROM postgres:18-trixie
@@ -8,4 +8,9 @@ RUN apt-get update \
     postgresql-18-postgis-3 \
     postgresql-18-postgis-3-scripts \
     postgresql-18-pgvector \
+    postgresql-18-hypopg \
   && rm -rf /var/lib/apt/lists/*
+
+# pg_stat_statements (statistics per query) works only when loaded at startup. A project that sets
+# its own command or shared_preload_libraries replaces this and adds it to its own list.
+CMD ["postgres", "-c", "shared_preload_libraries=pg_stat_statements"]
diff --git a/README.md b/README.md
index 384f66d..c0b4935 100644
--- a/README.md
+++ b/README.md
@@ -1,6 +1,6 @@
 # digib/postgres
 
-PostgreSQL 18 with PostGIS 3 and pgvector, the same image locally, in CI and deployed.
+PostgreSQL 18 with PostGIS 3, pgvector and hypopg, the same image locally, in CI and deployed.
 
 ```bash
 docker pull ghcr.io/digib/postgres:18
@@ -11,7 +11,8 @@ docker pull ghcr.io/digib/postgres:18
 - **[PostgreSQL 18](https://hub.docker.com/_/postgres)**, from the official `postgres:18-trixie` image: Debian, for x86 and Arm
 - **[PostGIS 3](https://postgis.net/)**, with its topology and Tiger geocoder extensions (`postgresql-18-postgis-3`, `postgresql-18-postgis-3-scripts`)
 - **[pgvector](https://github.com/pgvector/pgvector)** (`postgresql-18-pgvector`)
-- PostgreSQL's own extensions, such as `pg_trgm` and `fuzzystrmatch`
+- **[hypopg](https://hypopg.readthedocs.io/)** (`postgresql-18-hypopg`): hypothetical indexes, to see what an index would do without building it
+- PostgreSQL's own extensions, such as `pg_trgm`, `fuzzystrmatch` and `pg_stat_statements` (statistics per query), which the image loads at startup (`shared_preload_libraries`). A project that sets its own `command` or `shared_preload_libraries` replaces that and adds `pg_stat_statements` to its own list.
 
 Extensions come from the PostgreSQL project's apt repository, which follows each release. A project creates the ones it uses, in a migration or an init script: