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