Here's what rhymes with counterveil.
fail sale sail avail veil hail shale vale assail hale countervail faille male scale mail pale tail tale jail nail rail frail gale whale bail stale travail wail bale dale pail snail flail kale unveil wale detail trail prevail email curtail inhale quail quale bewail braille derail mainsail topsail grail taffrail wassail hightail carrell entail exhale gunwale pigtail foresail impale monorail bobtail pellmell lugsail fingernail ponytail martingale nonpareil hangnail swallowtail tattletale