diff --git a/hack/jenkins/e2e.sh b/hack/jenkins/e2e.sh
index c6e23b6854a..c74276f6055 100755
--- a/hack/jenkins/e2e.sh
+++ b/hack/jenkins/e2e.sh
@@ -105,6 +105,17 @@ GCE_FLAKY_TESTS=(
     "allows\sscheduling\sof\spods\son\sa\sminion\safter\sit\srejoins\sthe\scluster" # file: resize_nodes.go, issue: #13258
     )
 
+# The following tests are known to be slow running (> 2 min), and are
+# thus run only in their own -slow- build variants.  Note that tests
+# can be slow by explicit design (e.g. some soak tests), or slow
+# through poor implementation.  Please indicate which applies in the
+# comments below, and for poorly implemented tests, please quote the
+# issue number tracking speed improvements.
+GCE_SLOW_TESTS=(
+    "SchedulerPredicates\svalidates\sMaxPods\slimit " # 8 min,        file: scheduler_predicates.go, PR:    #13315
+    "Nodes\sResize"                                   # 3 min 30 sec, file: resize_nodes.go,         issue: #13323
+    )
+
 # Tests which are not able to be run in parallel.
 GCE_PARALLEL_SKIP_TESTS=(
     ${GCE_DEFAULT_SKIP_TESTS[@]:+${GCE_DEFAULT_SKIP_TESTS[@]}}
@@ -153,7 +164,7 @@ GCE_RELEASE_SKIP_TESTS=(
 
 # Define environment variables based on the Jenkins project name.
 case ${JOB_NAME} in
-  # Runs all non-flaky tests on GCE, sequentially.
+  # Runs all non-flaky, non-slow tests on GCE, sequentially.
   kubernetes-e2e-gce)
     : ${E2E_CLUSTER_NAME:="jenkins-gce-e2e"}
     : ${E2E_DOWN:="false"}
@@ -161,6 +172,7 @@ case ${JOB_NAME} in
     : ${GINKGO_TEST_ARGS:="--ginkgo.skip=$(join_regex_allow_empty \
           ${GCE_DEFAULT_SKIP_TESTS[@]:+${GCE_DEFAULT_SKIP_TESTS[@]}} \
           ${GCE_FLAKY_TESTS[@]:+${GCE_FLAKY_TESTS[@]}} \
+          ${GCE_SLOW_TESTS[@]:+${GCE_SLOW_TESTS[@]}} \
           )"}
     : ${KUBE_GCE_INSTANCE_PREFIX="e2e-gce"}
     : ${PROJECT:="k8s-jkns-e2e-gce"}
@@ -202,6 +214,18 @@ case ${JOB_NAME} in
     : ${PROJECT:="k8s-jkns-e2e-gce-flaky"}
     ;;
 
+  # Runs slow tests on GCE, sequentially.
+  kubernetes-e2e-gce-slow)
+    : ${E2E_CLUSTER_NAME:="jenkins-gce-e2e-slow"}
+    : ${E2E_DOWN:="false"}
+    : ${E2E_NETWORK:="e2e-slow"}
+    : ${GINKGO_TEST_ARGS:="--ginkgo.focus=$(join_regex_no_empty \
+          ${GCE_SLOW_TESTS[@]:+${GCE_SLOW_TESTS[@]}} \
+          )"}
+    : ${KUBE_GCE_INSTANCE_PREFIX:="e2e-slow"}
+    : ${PROJECT:="k8s-jkns-e2e-gce-slow"}
+    ;;
+
   # Runs all non-flaky tests on GCE in parallel.
   kubernetes-e2e-gce-parallel)
     : ${E2E_CLUSTER_NAME:="jenkins-gce-e2e-parallel"}