Here's what rhymes with pigmei.
                        
                        
                    
                                my  nigh  mai  muy  nai  mei  by  high  why  die  lie  thy  y  buy  cry  deny  guy  tie  vi  hi  shy  sigh  bi  bye  chi  dye  fi  hy  pi  pie  thai  thigh  vie  dei  ly  psi  quae  rye  ty  wir  awry  hai  lye  wry  cy  decry  fy  kai  lai  luy  sy  tai  thei  wai  phi  dry  try  fly  sky  defy  spy  fry  ply  sly  pry  tri  trie  belie  pri  untie  descry  dignify  sty  aquae  amebae  stye  lanai  drachmai  slier  apply  reply  thereby  imply  nearby  rely  comply  hereby  signify  goodbye  pupae  termini  terrify  typify  amoebae  edify  bonsai  deify  spry  triply  turfy  scurfy  shanghai  ripply  banzais  supply  occupy  whereby  modify  nuclei  specify  alkali  testify  verify  notify  underlie  alibi  magnify  nullify  pacify  rectify  samurai  unify  codify  liquefy  mollify  overlie  ramify  vilify  ossify  retry  vivify  blowfly  petrify  stupefy  liquify  barfly  mummify  prettify  overbuy  yuppify  identify  justify  satisfy  stimuli  clarify  qualify  classify  butterfly  certify  glorify  gratify  purify  quantify  amplify  fortify  ratify  standby  beautify  indemnify  lullaby  crucify  mortify  objectify  personify  acidify  detoxify  dragonfly  firefly  mystify  ultrahigh  calcify  horrify  misapply  reunify  cumuli  overfly  scarify  versify  declassify  vitrify  beatify  gentrify  speechify  dandify  multiply  simplify  exemplify  intensify  alveoli  diversify  disqualify  falsify  solidify  resupply  demystify  electrify  preoccupy  stratify  stultify  emulsify  revivify  dissatisfy  hyperbolae  refortify  syllabify  solemnify  oversupply  reclassify  misidentify  oversimplify  transmogrify