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 1 Spanish dessert for 24A (5)

 4 Plant finishes off beneath one particular shrub (4)

 6 Wise person’s 4A (4)

 9 A head in European capital turned for sovereign (7)

10 It’s modified inside to create what you’ll find right here: (7,3)

12 Partially pulverizes typewriter, like a 13 (5)

13 24A is ground, not minced (9)

14 Pair of sevens equal 29 (6)

16 Verify a young-looking parent’s age is 29 (8)

19 4A, arrogant crackpot (8)

21 Dr or Sgt. 13 (6)

24 This puzzle’s theme is “falling,” perhaps? (9)

25 Where you might find cardinals and spies: outside an ancient city (5)

26 Small prophet pursuing love in movements across boundaries (7)

27 Harris’s bird swallowing my half of loaf (7)

28 4A is pristine (4)

29 Incorrectly saw a germ (4)

30 Wealthy men hoarding 4A (5)

DOWN

 1 Makes light of Zen and teases viciously (7,2)

 2 Stomps wildly after inauguration of income taxes (7)

 3 Before the deadline, phonetically? (5)

 4 Laugh at people’s poet (6)

 5 European craze occupies Paul (8)

 7 Turner loses face with that guy, eating excellent kind of 21 (7)

 8 Leaders in Egypt justify extra costs, to boot (5)

11 Take in breath while filling most of toboggan (7)

15 “Fields of grass” commercial interrupts soundtrack of cat video? (7)

17 Strip dog of bit of meat to equip a Southern university (9)

18 Is one sun exploding? That’s not worth discussing (8)

20 Macho dude (male) ran erratically (4,3)

22 Talk about second 4A (7)

23 Yes, a sin (6)

24 Tempest (or maybe part of it) (5)

25 Reindeer nearly awaken (5)

SOLUTION TO PUZZLE NO. 3408

ACROSS 1 PATRO(LMA)N (mal anag.) 6 hidden 9 L + I’M IT 10 LAMINA (rev.) + TED 11 VERBA (anag.) + TIM 12 QUA + HOG 14 [b]RAKE 15 anag. 18 NEWAR[k] + RIVAL 19 A(GO)G 22 2 defs. 24 [v]O(DOME)TER 26 E(X IS TEN)CE (emcee alternate letters) 27 hidden 28 YEN + TA 29 anag.

DOWN 1 PAL + AVER 2 TOMB + R(OK)AW 3 O(UT)LAY 4 MUL(TIMED + I)A (alum rev.) 5 NUMB[er] 6 CON + QUE + RS 7 LAT(C)H 8 BODE + GAS 13 HO(WAR)D + SEND 16 SIGH + TREAD 17 anag. 18 anag. 20 anag. 21 I + MPOSE (anag.) 23 hidden 25 S(NO)W