diff --git a/bot/build.sh b/bot/build.sh
index 2b35c63551..17c48ab08b 100755
--- a/bot/build.sh
+++ b/bot/build.sh
@@ -103,6 +103,10 @@ echo "bot/build.sh: STORAGE='${STORAGE}'"
 # make sure ${STORAGE} exists
 mkdir -p ${STORAGE}
 
+# Make sure ${STORAGE} gets bind-mounted
+# This will make sure that any subsequent jobs that create dirs or files under STORAGE have access to it in the container
+export SINGULARITY_BIND="${SINGULARITY_BIND},${STORAGE}"
+
 # make sure the base tmp storage is unique
 JOB_STORAGE=$(mktemp --directory --tmpdir=${STORAGE} bot_job_tmp_XXX)
 echo "bot/build.sh: created unique base tmp storage directory at ${JOB_STORAGE}"
@@ -315,6 +319,9 @@ else
     TARBALL_STEP_ARGS+=("--resume" "${REMOVAL_TMPDIR}")
 fi
 
+# Make sure we define storage, so that the TMPDIR is set to this in eessi_container.sh
+TARBALL_STEP_ARGS+=("--storage" "${STORAGE}")
+
 timestamp=$(date +%s)
 # to set EESSI_VERSION we need to source init/eessi_defaults now
 source $software_layer_dir/init/eessi_defaults
diff --git a/easystacks/software.eessi.io/2023.06/accel/nvidia/zen4_h100/eessi-2023.06-eb-4.9.4-2023a-CUDA.yml b/easystacks/software.eessi.io/2023.06/accel/nvidia/zen4_h100/eessi-2023.06-eb-4.9.4-2023a-CUDA.yml
index 60d82d46ad..fbb9203fd2 100644
--- a/easystacks/software.eessi.io/2023.06/accel/nvidia/zen4_h100/eessi-2023.06-eb-4.9.4-2023a-CUDA.yml
+++ b/easystacks/software.eessi.io/2023.06/accel/nvidia/zen4_h100/eessi-2023.06-eb-4.9.4-2023a-CUDA.yml
@@ -2,3 +2,4 @@ easyconfigs:
   - CUDA-12.1.1.eb:
       options:
         accept-eula-for: CUDA
+  - pmt-1.2.0-GCCcore-12.3.0-CUDA-12.1.1.eb
diff --git a/eessi_container.sh b/eessi_container.sh
index d96ad041a8..d7f3dfa3ba 100755
--- a/eessi_container.sh
+++ b/eessi_container.sh
@@ -370,40 +370,41 @@ fi
 # 2. set up host storage/tmp if necessary
 # if session to be resumed from a previous one (--resume ARG) and ARG is a directory
 #   just reuse ARG, define environment variables accordingly and skip creating a new
-#   tmp storage
+#    eessi.XXXXXXXXXXX tempdir within TMPDIR
+
+# But before we call mktemp, we need to potentially set or create TMPDIR
+# as location for temporary data use in the following order
+#   a. command line argument -l|--host-storage
+#   b. env var TMPDIR
+#   c. /tmp
+# note, we ensure that (a) takes precedence by setting TMPDIR to STORAGE
+#     if STORAGE is not empty
+# note, (b) & (c) are automatically ensured by using 'mktemp -d --tmpdir' to
+#     create a temporary directory
+if [[ ! -z ${STORAGE} ]]; then
+  export TMPDIR=${STORAGE}
+  # mktemp fails if TMPDIR does not exist, so let's create it
+  mkdir -p ${TMPDIR}
+fi
+if [[ ! -z ${TMPDIR} ]]; then
+  # TODO check if TMPDIR already exists
+  # mktemp fails if TMPDIR does not exist, so let's create it
+  mkdir -p ${TMPDIR}
+fi
+if [[ -z ${TMPDIR} ]]; then
+  # mktemp falls back to using /tmp if TMPDIR is empty
+  # TODO check if /tmp is writable, large enough and usable (different
+  #      features for ro-access and rw-access)
+  [[ ${VERBOSE} -eq 1 ]] && echo "skipping sanity checks for /tmp"
+fi
+
+# Now, set the EESSI_HOST_STORAGE either baed on the resumed directory, or create a new one with mktemp
 if [[ ! -z ${RESUME} && -d ${RESUME} ]]; then
   # resume from directory ${RESUME}
   #   skip creating a new tmp directory, just set environment variables
   echo "Resuming from previous run using temporary storage at ${RESUME}"
   EESSI_HOST_STORAGE=${RESUME}
 else
-  # we need a tmp location (and possibly init it with ${RESUME} if it was not
-  #   a directory
-
-  # as location for temporary data use in the following order
-  #   a. command line argument -l|--host-storage
-  #   b. env var TMPDIR
-  #   c. /tmp
-  # note, we ensure that (a) takes precedence by setting TMPDIR to STORAGE
-  #     if STORAGE is not empty
-  # note, (b) & (c) are automatically ensured by using 'mktemp -d --tmpdir' to
-  #     create a temporary directory
-  if [[ ! -z ${STORAGE} ]]; then
-    export TMPDIR=${STORAGE}
-    # mktemp fails if TMPDIR does not exist, so let's create it
-    mkdir -p ${TMPDIR}
-  fi
-  if [[ ! -z ${TMPDIR} ]]; then
-    # TODO check if TMPDIR already exists
-    # mktemp fails if TMPDIR does not exist, so let's create it
-    mkdir -p ${TMPDIR}
-  fi
-  if [[ -z ${TMPDIR} ]]; then
-    # mktemp falls back to using /tmp if TMPDIR is empty
-    # TODO check if /tmp is writable, large enough and usable (different
-    #      features for ro-access and rw-access)
-    [[ ${VERBOSE} -eq 1 ]] && echo "skipping sanity checks for /tmp"
-  fi
   EESSI_HOST_STORAGE=$(mktemp -d --tmpdir eessi.XXXXXXXXXX)
   echo "Using ${EESSI_HOST_STORAGE} as tmp directory (to resume session add '--resume ${EESSI_HOST_STORAGE}')."
 fi
@@ -423,7 +424,14 @@ fi
 
 # if ${RESUME} is a file (assume a tgz), unpack it into ${EESSI_HOST_STORAGE}
 if [[ ! -z ${RESUME} && -f ${RESUME} ]]; then
-  tar xf ${RESUME} -C ${EESSI_HOST_STORAGE}
+  if [[ "${RESUME}" == *.tgz ]]; then
+    tar xf ${RESUME} -C ${EESSI_HOST_STORAGE}
+  # Add support for resuming from zstd-compressed tarballs
+  elif [[ "${RESUME}" == *.zst && -x "$(command -v zstd)" ]]; then
+    zstd -dc ${RESUME} | tar -xf - -C ${EESSI_HOST_STORAGE}
+  elif [[ "${RESUME}" == *.zst && ! -x "$(command -v zstd)" ]]; then
+    fatal_error "Trying to resume from tarball ${RESUME} which was compressed using zstd, but zstd command not found"
+  fi
   echo "Resuming from previous run using temporary storage ${RESUME} unpacked into ${EESSI_HOST_STORAGE}"
 fi