Across:
   1. Entice prime suspect to accept new assurance (12)
   8. Girl from South America’s inspection (7)
   9. Odd man I smashed with rock! (7)
  11. Love cheat Carol and I took apart, in a manner of speaking (10)
  12. Band sit back in elevator (4)
  14. Try out new first tee (4 4)
  16. Actor circles around river (6)
  17. Boy has tea without any sugar initially (3)
  19. Small change a sister holds now... (6)
  21. ...Small amount can heal over time (8)
  24. You and me are captivated by saucy heartless girl (4)
  25. Drama quote developed by question-master (10)
  27. Propose you and me return leading horse on East Street (7)
  28. Best pail Tom broke! (7)
  29. In seconds, group went outside with nothing (12)
Down:
   1. Dorian’s strange advances (7)
   2. Two jobs in communications business (4 6)
   3. They race everyone that is in posh cars (8)
   4. Popular princess gets object from the sub-continent (6)
   5. Scholar is in the old retro marketplace (4)
   6. Ground corn out to make a bit of bread (7)
   7. They jump in and madly spurt poison over Turkish leader! (12)
  10. Make useless internal hiding place easy to find (12)
  13. Reproduces porter’s ace manoeuvre (10)
  16. Take back the addled egg starters (3)
  18. Wrongly report mosque IT breakdown (8)
  20. Missile on one ship, say, may be top quality (7)
  22. Not injured, not hot, and not packing (7)
  23. Periods when no night flyers go outside (6)
  26. Lend a hand to head off puppy (4)