Here's what rhymes with unmincing.
                        
                        
                    
                                mincing  rinsing  wincing  convincing  evincing  unconvincing  Words that almost rhyme with unmincing
missing  mixing  minting  winning  fixing  kissing  piercing  knitting  milling  nearing  thinning  hinting  hissing  lynching  milking  pinching  pinning  sinning  ginning  nipping  building  living  giving  sitting  willing  filling  fishing  fitting  killing  printing  singing  lifting  listing  picking  shifting  shipping  spinning  unwilling  wishing  admitting  bidding  digging  fearing  hitting  rearing  ringing  billing  cheering  chilling  dipping  emitting  grinning  kicking  omitting  pitching  rigging  shearing  shilling  sibling  whipping  whistling  filming  gearing  kidding  kindling  licking  pitting  ripping  risking  sifting  sipping  sniffing  ticking  tilting  tipping  chipping  cringing  fiddling  fringing  gilding  impinging  ridding  searing  smearing  sneering  tickling  tiling  tilling  twinning  unflinching  unwitting  wringing  affixing  chiming  consigning  dimming  flinching  glinting  hitching  leering  lilting  lisping  pickling  sieving  silting  skinning  veering  whittling  whizzing  wilting  winging  beginning  thinking  bringing  appearing  consisting  clearing  linking  permitting  sinking  swimming  switching  assisting  clinging  committing  drifting  drilling  insisting  slipping  steering  sticking  swinging  twisting  adhering  bridging  clicking  clipping  dismissing  dripping  quitting  submitting  thrilling  enlisting  enriching  flinging  flitting  gripping  skimming  skipping  spilling  spitting  stinging  stitching  trickling  trimming  tripping  twitching  underpinning  unremitting  unthinking  afflicting  brimming  flicking  flipping  imprinting  infringing  limping  pricking  quilting  remitting  squinting  winking  abridging  convicting  eclipsing  grilling  incising  nonliving  reminiscing  skidding  slinging  slitting  spearing  splinting  sprinting  sufficing  swindling  swishing  existing  drinking  engineering  conflicting  depicting  forbidding  pioneering  resisting  splitting  springing  transmitting  forgiving  inflicting  persisting  rebuilding  shrinking  stripping  befitting  blinking  domineering  equipping  positing  stinking  subsisting  bewitching  instilling  misgiving  reprinting  scripting  stringing  unforgiving  agonising  clinking  minimising  refilling  refitting  reliving  stripling  unblinking  fulfilling  interfering  predicting  sprinkling  thanksgiving  distilling  persevering  rethinking  volunteering  constricting  maximising  mountaineering  reappearing  disappearing  restricting  coexisting  counterfeiting  preexisting  contradicting  criticising  electioneering  profiteering