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ACROSS

 1 “High and low openings on either side of zoo!” I rant in a random way (like
this entry) (10)

 6 At first, detectives have, like, half of this puzzle’s entries (4)

10 Dazed maestro puts animated segment backward (2,1,6)

11 Support includes a bit of love, like the space left of this entry (5)

12 Medium gets into unraveling mystery feature of this diagram (8)

13 Absurdly, anoint this puzzle’s publisher (6)

15 Disrupt usual parties… (5)

17 …oblique fiestas serving melts (9)

19 Impala, for instance, eaten by monstrous iguana in a foreign country (9)

21 Desert’s middle, so they say (5)

22 A hybrid, like half of this puzzle’s entries (6)

23 Voltaire originally revised article that’s unlike this entry (8)

26 Having secured a blockbuster, we like the unfilled parts of this diagram (5)

27 Court regular prints one novel (6,3)

28 No German announced the number of clues that reference some aspect of
this puzzle, not counting this one (4)

29 Test-taking heavyweight holding pig, like this entry and 25 (10)

DOWN

 1 Do establishment broadcasts in disk entertain, finally? (4,5)

 2 Give more weapons to rebellious Estonians approaching Russian military
fronts (5)

 3 That woman is covered with pimples—things you might pick? (7)

 4 Hey—prolong arcane organ study (10)

 5 Restaurant has atmosphere (4)

 7 Obscure qualities in the heart of Altoona, Scranton, and Allentown (9)

 8 No relatives returned a camera (5)

 9 A slice of banana loaf is on fire (6)

14 Screw up when taking live measurement (6,4)

16 Hard-rock band lacking drive, or a singer with a musical instrument (9)

18 Something you could use to clean a chair’s outside: fish whiskers,
initially (5,4)

20 A bird drops an egg in a roll (6)

21 Aware of faction that keeps Romney without leadership (7)

22 Egyptian city is no ruddier (5)

24 Lewis and Peter form a TV channel (1-4)

25 Preeminent informers turning up (4)

SOLUTION TO PUZZLE NO. 3387

ACROSS 1 anag. 6 HA + DJ 9 NEP (rev.) + TUNE 10 T[rend]Y + PICA + L 12 A + S + SET 13 HOR[n] + SEW + HIP 14 anag.
15 CAB(RIO)LE 18 B + ROOK + L + Y + N 20 2 defs. 23 SA (rev.) + LESS LIP
25 SO + LID 26 ROPES(I)N (person anag.)
27 R + HOM[e] + BIC 28 2 defs. 29 pun

DOWN 1 PEN(Z)ANCE 2 OP(POS)ED (sop rev.) 3 anag. 4 triple anag. 5 hidden
7 AL(COHO)L 8 JA(LOP)Y 11 anag.
16 BON(APART)E 17 P(ROD)UCER
19 RELAP (rev.) + S[tar]E 21 H(ALI + B)UT
22 TSUR (rev.) + IS 24 hidden