diff --git a/DOCKER_AND_COMPOSE_VERSION_MATRIX b/DOCKER_AND_COMPOSE_VERSION_MATRIX
index ed25e6e..e9c524c 100644
--- a/DOCKER_AND_COMPOSE_VERSION_MATRIX
+++ b/DOCKER_AND_COMPOSE_VERSION_MATRIX
@@ -1,3 +1,2 @@
 latest
-20    1.29.*
 20.10 1.29.*
diff --git a/README.md b/README.md
index 938539b..09db9d4 100644
--- a/README.md
+++ b/README.md
@@ -10,10 +10,10 @@ This is very useful for CI pipelines, which leverage "Docker in Docker".
 
 ## Docker versions supported
 
-There are versions based on different docker versions, e.g. `latest`, `20.10`, `19.03` and `19`.
+Note: In the past. this docker image (tags) focused on the docker version (e.g. `latest`, `20.10`, `19.03` and `19`).
+But as the docker releases got less disruptive, the approach changes to use the docker compose version as tags.
 
-docker-compose matches the latest version compatible with the respective docker release.
-Eg, `20.10` includes docker-compose 1.27.4. The `latest` tag always includes the latest docker-compose build.
+The Docker Compose versions supported here use the most recent docker version compatible with it.
 
 All available Docker Engine versions and the respective Docker Compose versions are defined in [`DOCKER_AND_COMPOSE_VERSION_MATRIX`](./DOCKER_AND_COMPOSE_VERSION_MATRIX).
 
diff --git a/hooks/build b/hooks/build
index 9b6f10f..e989008 100755
--- a/hooks/build
+++ b/hooks/build
@@ -1,10 +1,17 @@
 #!/usr/bin/env sh
 
-set -ex
+set -e
 
 while read -r docker_version compose_version;
 do
-  image=${DOCKER_REPO}:${docker_version}
+  if [ -z "${compose_version}" ]
+  then
+    tag="latest"
+  else
+    tag="${compose_version%.*}"
+  fi
+  image=${DOCKER_REPO}:${tag}
+
   echo "# Building image ${image}..."
 
   docker build \
diff --git a/hooks/push b/hooks/push
index 3fba919..05829c9 100755
--- a/hooks/push
+++ b/hooks/push
@@ -1,10 +1,17 @@
 #!/usr/bin/env sh
 
-set -ex
+set -e
 
-while read -r docker_version _;
+while read -r _ compose_version;
 do
-  image=${DOCKER_REPO}:${docker_version}
+  if [ -z "${compose_version}" ]
+  then
+    tag="latest"
+  else
+    tag="${compose_version%.*}"
+  fi
+  image=${DOCKER_REPO}:${tag}
+
   echo "# Pushing image ${image}..."
 
   docker image push "${image}"
diff --git a/hooks/test b/hooks/test
index 1e7f047..bb5adcb 100755
--- a/hooks/test
+++ b/hooks/test
@@ -1,10 +1,17 @@
 #!/usr/bin/env sh
 
-set -ex
+set -e
 
-while read -r docker_version _;
+while read -r docker_version compose_version;
 do
-  image=${DOCKER_REPO}:${docker_version}
+  if [ -z "${compose_version}" ]
+  then
+    tag="latest"
+  else
+    tag="${compose_version%.*}"
+  fi
+  image=${DOCKER_REPO}:${tag}
+
   echo "# Testing image ${image}..."
   export IMAGE_NAME="${image}"