diff --git a/t/t5608-clone-2gb.sh b/t/t5608-clone-2gb.sh
index 4f8a95ddda411c..86994beccb472d 100755
--- a/t/t5608-clone-2gb.sh
+++ b/t/t5608-clone-2gb.sh
@@ -49,7 +49,7 @@ test_expect_success 'clone - with worktree, file:// protocol' '
 
 '
 
-test_expect_success SIZE_T_IS_64BIT,EXPENSIVE 'set up repo with >4GB object' '
+test_expect_success SIZE_T_IS_64BIT,LONG_IS_64BIT,EXPENSIVE 'set up repo with >4GB object' '
 	large_blob_size=$((4*1024*1024*1024+1)) &&
 	git init --bare 4gb-repo &&
 	head_oid=$(test-tool synthesize pack \
@@ -60,7 +60,7 @@ test_expect_success SIZE_T_IS_64BIT,EXPENSIVE 'set up repo with >4GB object' '
 	git -C 4gb-repo symbolic-ref HEAD refs/heads/main
 '
 
-test_expect_success SIZE_T_IS_64BIT,EXPENSIVE 'clone >4GB object via unpack-objects' '
+test_expect_success SIZE_T_IS_64BIT,LONG_IS_64BIT,EXPENSIVE 'clone >4GB object via unpack-objects' '
 	# The synthesized pack has five objects, so a large unpack limit keeps
 	# fetch-pack on the unpack-objects path.
 	git -c fetch.unpackLimit=100 clone --bare \
@@ -76,7 +76,7 @@ test_expect_success SIZE_T_IS_64BIT,EXPENSIVE 'clone >4GB object via unpack-obje
 	test "$source_blob" = "$clone_blob"
 '
 
-test_expect_success SIZE_T_IS_64BIT,EXPENSIVE 'clone with >4GB object via index-pack' '
+test_expect_success SIZE_T_IS_64BIT,LONG_IS_64BIT,EXPENSIVE 'clone with >4GB object via index-pack' '
 	# Force fetch-pack to hand the pack to index-pack instead.
 	git -c fetch.unpackLimit=1 clone --bare \
 		"file://$(pwd)/4gb-repo" 4gb-clone-index &&
diff --git a/t/t7508-status.sh b/t/t7508-status.sh
index c2057bc94c38c1..895945f3990226 100755
--- a/t/t7508-status.sh
+++ b/t/t7508-status.sh
@@ -1773,7 +1773,7 @@ test_expect_success 'slow status advice when core.untrackedCache true, and fsmon
 	)
 '
 
-test_expect_success EXPENSIVE 'status does not re-read unchanged 4 or 8 GiB file' '
+test_expect_success LONG_IS_64BIT,EXPENSIVE 'status does not re-read unchanged 4 or 8 GiB file' '
 	(
 		mkdir large-file &&
 		cd large-file &&