diff --git a/EESSI-install-software.sh b/EESSI-install-software.sh
index 7821655c07..4c85fdfc31 100755
--- a/EESSI-install-software.sh
+++ b/EESSI-install-software.sh
@@ -251,9 +251,14 @@ fi
 
 temp_install_storage=${TMPDIR}/temp_install_storage
 mkdir -p ${temp_install_storage}
+# Note the eessi...CUDA.yml file(s) is(are) copied by 'install_scripts.sh' from
+# the EESSI/software-layer easystacks/software.eessi.io/2023.06/accel/nvidia
+# directory to /cvmfs to avoid keeping them in sync manually. If more than one
+# such file is used (e.g., because different EasyBuild versions were used), the
+# install script 'install_cuda_and_libraries.sh' has to be run multiple times.
 if [ -z "${skip_cuda_install}" ] || [ ! "${skip_cuda_install}" ]; then
     ${EESSI_PREFIX}/scripts/gpu_support/nvidia/install_cuda_and_libraries.sh \
-        -e ${EESSI_PREFIX}/scripts/gpu_support/nvidia/eessi-2023.06-cuda-and-libraries.yml \
+        -e ${EESSI_PREFIX}/scripts/gpu_support/nvidia/eessi-2023.06-eb-4.9.4-2023a-CUDA.yml \
         -t ${temp_install_storage} \
         --accept-cuda-eula
 else
diff --git a/easystacks/software.eessi.io/2023.06/accel/nvidia/eessi-2023.06-eb-4.9.4-2023a-CUDA.yml b/easystacks/software.eessi.io/2023.06/accel/nvidia/eessi-2023.06-eb-4.9.4-2023a-CUDA.yml
index d54780804b..873c19aa33 100644
--- a/easystacks/software.eessi.io/2023.06/accel/nvidia/eessi-2023.06-eb-4.9.4-2023a-CUDA.yml
+++ b/easystacks/software.eessi.io/2023.06/accel/nvidia/eessi-2023.06-eb-4.9.4-2023a-CUDA.yml
@@ -1,2 +1,3 @@
 easyconfigs:
+  - CUDA-12.1.1.eb
   - cuDNN-8.9.2.26-CUDA-12.1.1.eb
diff --git a/install_scripts.sh b/install_scripts.sh
index df9bda3ad3..ad73e769dd 100755
--- a/install_scripts.sh
+++ b/install_scripts.sh
@@ -122,13 +122,23 @@ copy_files_by_list ${TOPDIR}/scripts ${INSTALL_PREFIX}/scripts "${script_files[@
 
 # Copy files for the scripts/gpu_support/nvidia directory
 nvidia_files=(
-    eessi-2023.06-cuda-and-libraries.yml
     install_cuda_and_libraries.sh
     install_cuda_host_injections.sh
     link_nvidia_host_libraries.sh
 )
 copy_files_by_list ${TOPDIR}/scripts/gpu_support/nvidia ${INSTALL_PREFIX}/scripts/gpu_support/nvidia "${nvidia_files[@]}"
 
+# special treatment for the easystack file(s) that lists CUDA and cu* libraries
+# To be picked up by a build job they have to be stored under
+# easystacks/software.eessi.io/2023.06/accel/nvidia/ on GitHub.
+# To avoid keeping that file and the one that we distribute via CernVM-FS so
+# users/sites can install the full CUDA SDK and cu* libraries under
+# 'host_injections' we copy the above file to the right location under /cvmfs.
+nvidia_host_injections_files=(
+    eessi-2023.06-eb-4.9.4-2023a-CUDA.yml
+)
+copy_files_by_list ${TOPDIR}/easystacks/software.eessi.io/2023.06/accel/nvidia ${INSTALL_PREFIX}/scripts/gpu_support/nvidia "${nvidia_host_injections_files[@]}"
+
 # Copy over EasyBuild hooks file used for installations
 hook_files=(
     eb_hooks.py
diff --git a/scripts/gpu_support/nvidia/eessi-2023.06-cuda-and-libraries.yml b/scripts/gpu_support/nvidia/eessi-2023.06-cuda-and-libraries.yml
deleted file mode 100644
index e0e47bf2d8..0000000000
--- a/scripts/gpu_support/nvidia/eessi-2023.06-cuda-and-libraries.yml
+++ /dev/null
@@ -1,3 +0,0 @@
-easyconfigs:
- - CUDA-12.1.1.eb
- - cuDNN-8.9.2.26-CUDA-12.1.1.eb