diff --git a/lib/galaxy/config/sample/job_conf.sample.yml b/lib/galaxy/config/sample/job_conf.sample.yml
index 3e11fa7582b6..55706e75be47 100644
--- a/lib/galaxy/config/sample/job_conf.sample.yml
+++ b/lib/galaxy/config/sample/job_conf.sample.yml
@@ -737,6 +737,30 @@ execution:
         # clusters. These don't need to be available on the Galaxy server
         # itself.
 
+    # Under most runners, Galaxy will set the `$GALAXY_SLOTS` environment variable in the
+    # tool execution environment to the number of cores allocated to the job by the
+    # scheduler. Tools can use this to control how many threads or processes they start.
+    #
+    # Under some runners, most notably Slurm and SGE, Galaxy will set environment
+    # variables related to the amount of memory allocated to the job by the scheduler, if
+    # possible. These are `$GALAXY_MEMORY_MB`, `$GALAXY_MEMORY_GB`,
+    # `$GALAXY_MEMORY_MB_PER_SLOT`, and `$GALAXY_MEMORY_GB_PER_SLOT`. You can override
+    # these on a per-environment basis as shown below.
+    #
+    # Additionally, you can specify two variables that will indicate a tool should use
+    # less memory than allocated. Typically some overhead is required or else the Linux
+    # OOM Killer will simply kill the job's processes if they exceed they amount of memory
+    # allocated by the scheduler.
+    job_vars_example:
+      runner: drmaa
+      env:
+        # Sets `$GALAXY_MEMORY_MB` to 2GB less than what has been allocated
+        - name: GALAXY_MEMORY_MB_OVERHEAD
+          value: "2048"
+        # Floor value for `$GALAXY_MEMORY_MB` if (allocated - overhead < floor)
+        - name: GALAXY_MEMORY_MB_FLOOR
+          value: "1024"
+
     # Following three environments demonstrate setting up per-job temp directory handling.
     # In these cases TEMP, TMP, and TMPDIR will be set for each job dispatched to these
     # environments.
diff --git a/lib/galaxy/jobs/runners/util/job_script/MEMORY_STATEMENT_TEMPLATE.sh b/lib/galaxy/jobs/runners/util/job_script/MEMORY_STATEMENT_TEMPLATE.sh
index a04087672bd1..20cbe2094364 100644
--- a/lib/galaxy/jobs/runners/util/job_script/MEMORY_STATEMENT_TEMPLATE.sh
+++ b/lib/galaxy/jobs/runners/util/job_script/MEMORY_STATEMENT_TEMPLATE.sh
@@ -5,10 +5,27 @@ if [ -n "$SGE_HGR_h_vmem" ]; then
     GALAXY_MEMORY_MB_PER_SLOT=`echo "$SGE_HGR_h_vmem" | sed 's/G$/ * 1024/' | bc | cut -d"." -f1` 2>$metadata_directory/memory_statement.log
 fi
 
+if [ -n "$GALAXY_MEMORY_MB" -a -n "${GALAXY_MEMORY_MB_OVERHEAD:-}" ]; then
+    GALAXY_MEMORY_MB=$(($GALAXY_MEMORY_MB - GALAXY_MEMORY_MB_OVERHEAD))
+    [ "$GALAXY_MEMORY_MB" -gt "${GALAXY_MEMORY_MB_FLOOR:=256}" ] || GALAXY_MEMORY_MB=$GALAXY_MEMORY_MB_FLOOR
+fi
+
 if [ -z "$GALAXY_MEMORY_MB_PER_SLOT" -a -n "$GALAXY_MEMORY_MB" ]; then
     GALAXY_MEMORY_MB_PER_SLOT=$(($GALAXY_MEMORY_MB / $GALAXY_SLOTS))
 elif [ -z "$GALAXY_MEMORY_MB" -a -n "$GALAXY_MEMORY_MB_PER_SLOT" ]; then
     GALAXY_MEMORY_MB=$(($GALAXY_MEMORY_MB_PER_SLOT * $GALAXY_SLOTS))
 fi
+
+if [ -n "$GALAXY_MEMORY_MB" -a -z "$GALAXY_MEMORY_GB" ]; then
+    GALAXY_MEMORY_GB=$(($GALAXY_MEMORY_MB / 1024))
+    [ "$GALAXY_MEMORY_GB" -gt 0 ] || GALAXY_MEMORY_GB=1
+fi
+if [ -n "$GALAXY_MEMORY_GB" -a -z "$GALAXY_MEMORY_GB_PER_SLOT" ]; then
+    GALAXY_MEMORY_GB_PER_SLOT=$(($GALAXY_MEMORY_GB / $GALAXY_SLOTS))
+    [ "$GALAXY_MEMORY_GB_PER_SLOT" -gt 0 ] || GALAXY_MEMORY_GB_PER_SLOT=1
+fi
+
 [ "${GALAXY_MEMORY_MB--1}" -gt 0 ] 2>>$metadata_directory/memory_statement.log && export GALAXY_MEMORY_MB || unset GALAXY_MEMORY_MB
 [ "${GALAXY_MEMORY_MB_PER_SLOT--1}" -gt 0 ] 2>>$metadata_directory/memory_statement.log && export GALAXY_MEMORY_MB_PER_SLOT || unset GALAXY_MEMORY_MB_PER_SLOT
+[ "${GALAXY_MEMORY_GB--1}" -gt 0 ] 2>>$metadata_directory/memory_statement.log && export GALAXY_MEMORY_GB || unset GALAXY_MEMORY_GB
+[ "${GALAXY_MEMORY_GB_PER_SLOT--1}" -gt 0 ] 2>>$metadata_directory/memory_statement.log && export GALAXY_MEMORY_GB_PER_SLOT || unset GALAXY_MEMORY_GB_PER_SLOT