diff --git a/tests/zfs-tests/tests/functional/pool_checkpoint/checkpoint_big_rewind.ksh b/tests/zfs-tests/tests/functional/pool_checkpoint/checkpoint_big_rewind.ksh
index f915d2ad41..7e523ef908 100755
--- a/tests/zfs-tests/tests/functional/pool_checkpoint/checkpoint_big_rewind.ksh
+++ b/tests/zfs-tests/tests/functional/pool_checkpoint/checkpoint_big_rewind.ksh
@@ -52,6 +52,7 @@ fragment_after_checkpoint_and_verify
 log_must zpool export $NESTEDPOOL
 log_must zpool import -d $FILEDISKDIR --rewind-to-checkpoint $NESTEDPOOL
 
-log_must zdb $NESTEDPOOL
+log_must zpool export $NESTEDPOOL
+log_must zdb -e -p $FILEDISKDIR $NESTEDPOOL
 
 log_pass "Rewind to checkpoint on a stressed pool."
diff --git a/tests/zfs-tests/tests/functional/pool_checkpoint/checkpoint_capacity.ksh b/tests/zfs-tests/tests/functional/pool_checkpoint/checkpoint_capacity.ksh
index 15afc4adf4..b6d34307b3 100755
--- a/tests/zfs-tests/tests/functional/pool_checkpoint/checkpoint_capacity.ksh
+++ b/tests/zfs-tests/tests/functional/pool_checkpoint/checkpoint_capacity.ksh
@@ -80,13 +80,14 @@ log_mustnot dd if=/dev/urandom of=$NESTEDFS0FILE bs=1M count=300
 #
 log_must zpool list $NESTEDPOOL
 
-log_must zdb -kc $NESTEDPOOL
-
 log_must zpool export $NESTEDPOOL
+log_must zdb -e -p $FILEDISKDIR -kc $NESTEDPOOL
+
 log_must zpool import -d $FILEDISKDIR --rewind-to-checkpoint $NESTEDPOOL
 
 log_must [ "$(head -c 100 $NESTEDFS0FILE)" = "$FILE0INTRO" ]
 
-log_must zdb $NESTEDPOOL
+log_must zpool export $NESTEDPOOL
+log_must zdb -e -p $FILEDISKDIR $NESTEDPOOL
 
 log_pass "Do not reuse checkpointed space at low capacity."
diff --git a/tests/zfs-tests/tests/functional/pool_checkpoint/checkpoint_discard_busy.ksh b/tests/zfs-tests/tests/functional/pool_checkpoint/checkpoint_discard_busy.ksh
index ae099ff270..f970935f5b 100755
--- a/tests/zfs-tests/tests/functional/pool_checkpoint/checkpoint_discard_busy.ksh
+++ b/tests/zfs-tests/tests/functional/pool_checkpoint/checkpoint_discard_busy.ksh
@@ -104,7 +104,8 @@ set_tunable64 SPA_DISCARD_MEMORY_LIMIT 16777216
 
 nested_wait_discard_finish
 
-log_must zdb $NESTEDPOOL
+log_must zpool export $NESTEDPOOL
+log_must zdb -e -p $FILEDISKDIR $NESTEDPOOL
 
 log_pass "Can export/import but not rewind/checkpoint/discard or " \
     "change pool's config while discarding."
diff --git a/tests/zfs-tests/tests/functional/pool_checkpoint/pool_checkpoint.kshlib b/tests/zfs-tests/tests/functional/pool_checkpoint/pool_checkpoint.kshlib
index ea6c03e9d5..bb8bab6cdf 100644
--- a/tests/zfs-tests/tests/functional/pool_checkpoint/pool_checkpoint.kshlib
+++ b/tests/zfs-tests/tests/functional/pool_checkpoint/pool_checkpoint.kshlib
@@ -154,13 +154,18 @@ function setup_nested_pools
 
 function cleanup_nested_pool
 {
-	log_must zpool destroy $NESTEDPOOL
+	if poolexists $NESTEDPOOL; then
+		log_must zpool destroy $NESTEDPOOL
+	fi
+
 	log_must rm -f $FILEDISKS
 }
 
 function cleanup_test_pool
 {
-	log_must zpool destroy $TESTPOOL
+	if poolexists $TESTPOOL; then
+		log_must zpool destroy $TESTPOOL
+	fi
 
 	#
 	# We always clear the labels of all disks