diff --git a/t/lib-httpd.sh b/t/lib-httpd.sh
index 782891908d..1f6b9b08d1 100644
--- a/t/lib-httpd.sh
+++ b/t/lib-httpd.sh
@@ -29,7 +29,7 @@
 # Copyright (c) 2008 Clemens Buchacher <drizzd@aon.at>
 #
 
-if test -n "$NO_CURL"
+if ! test_have_prereq LIBCURL
 then
 	skip_all='skipping test, git built without http support'
 	test_done
diff --git a/t/t5516-fetch-push.sh b/t/t5516-fetch-push.sh
index dedca106a7..c1220b2ed3 100755
--- a/t/t5516-fetch-push.sh
+++ b/t/t5516-fetch-push.sh
@@ -1834,7 +1834,7 @@ test_expect_success 'refuse to push a hidden ref, and make sure do not pollute t
 	test_dir_is_empty testrepo/.git/objects/pack
 '
 
-test_expect_success 'fetch warns or fails when using username:password' '
+test_expect_success LIBCURL 'fetch warns or fails when using username:password' '
 	message="URL '\''https://username:<redacted>@localhost/'\'' uses plaintext credentials" &&
 	test_must_fail git -c fetch.credentialsInUrl=allow fetch https://username:password@localhost 2>err &&
 	! grep "$message" err &&
@@ -1853,7 +1853,7 @@ test_expect_success 'fetch warns or fails when using username:password' '
 '
 
 
-test_expect_success 'push warns or fails when using username:password' '
+test_expect_success LIBCURL 'push warns or fails when using username:password' '
 	message="URL '\''https://username:<redacted>@localhost/'\'' uses plaintext credentials" &&
 	test_must_fail git -c fetch.credentialsInUrl=allow push https://username:password@localhost 2>err &&
 	! grep "$message" err &&
diff --git a/t/t5601-clone.sh b/t/t5601-clone.sh
index d2f046b4b9..eeed233362 100755
--- a/t/t5601-clone.sh
+++ b/t/t5601-clone.sh
@@ -71,7 +71,7 @@ test_expect_success 'clone respects GIT_WORK_TREE' '
 
 '
 
-test_expect_success 'clone warns or fails when using username:password' '
+test_expect_success LIBCURL 'clone warns or fails when using username:password' '
 	message="URL '\''https://username:<redacted>@localhost/'\'' uses plaintext credentials" &&
 	test_must_fail git -c fetch.credentialsInUrl=allow clone https://username:password@localhost attempt1 2>err &&
 	! grep "$message" err &&
@@ -89,7 +89,7 @@ test_expect_success 'clone warns or fails when using username:password' '
 	test_line_count = 1 warnings
 '
 
-test_expect_success 'clone does not detect username:password when it is https://username@domain:port/' '
+test_expect_success LIBCURL 'clone does not detect username:password when it is https://username@domain:port/' '
 	test_must_fail git -c fetch.credentialsInUrl=warn clone https://username@localhost:8080 attempt3 2>err &&
 	! grep "uses plaintext credentials" err
 '
diff --git a/t/test-lib.sh b/t/test-lib.sh
index f5291ef56e..55857af601 100644
--- a/t/test-lib.sh
+++ b/t/test-lib.sh
@@ -1572,6 +1572,7 @@ esac
 test_set_prereq REFFILES
 
 ( COLUMNS=1 && test $COLUMNS = 1 ) && test_set_prereq COLUMNS_CAN_BE_1
+test -z "$NO_CURL" && test_set_prereq LIBCURL
 test -z "$NO_PERL" && test_set_prereq PERL
 test -z "$NO_PTHREADS" && test_set_prereq PTHREADS
 test -z "$NO_PYTHON" && test_set_prereq PYTHON