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ACROSS

 1 Name one independent state in the Middle East (5)

 4 Showed compassion in play about decent orchestra space (4,4)

 9 Aviator-poets tilt wildly (4,5)

10 Container vessel carrying organic fiber (5)

11 How to improve your aim: Slander cop and appear in charge (6,8)

13 See 4D

14 Collaborator’s outside of the audio device with a hen (4,6)

17 Percussionist and bandleader connect around best arrangement of tune (4,6)

19 One old lunatic’s object of worship (4)

22 Type of publication in which agent mimicked skill? (5,9)

25 Expected Eliot’s performances by two (5)

26 Throw it in reverse to get old sheet just beneath the cover? (5,4)

28 Right-wingers retreating, but taking apart… (3,5)

29 …dwelling found in eight Across entries? (5)

DOWN

 1 Department of Treasury statement: “Leaders connect these to find out what is really going on” (4)

 2 Crashed Saab with Tim Rice (7)

 3 Attack demon with broken gun (6)

 4 and 13A Long live rent rollback in city (3,4)

 5 Swimmer is warmer after removing cap (5)

 6 Redesign help icon for game (8)

 7 Scare Gilliam when accepting condition (7)

 8 Life, for instance, overwhelms extremely bitter intellectual (8)

12 One of two comforting words that would timelessly turn into its opposite (5)

13 Absurdly, audit pet talent (8)

15 Dull toy company cuts its losses (5)

16 Kitty, making a case for profound returns, moves more quickly (6,2)

18 Capture effortlessness when announcing circus routine (7)

20 French artist in Berlin: “You set upon the winner” (7)

21 First-rate, hallowed, and maximally proficient… (6)

23 …flower expert is discovered (5)

24 Jump from plane, using parachute at the end (4)

27 Judge is oddly tardy (3)

SOLUTION TO PUZZLE NO. 3525