Ultrasounds, 20 kHz at power d. of 6.7 W/g acetone, were added cont. or pulsed for 0.2 of every second, to assist acetone to condense, with 100% selectivity, to 4-methyl-4hydroxy-2-pentanone (DAA) in 5.7, 9.1% yields over MgO (3/30, 30 C/5 min) and 2.7,4.1% over Ba(OH)(2).8H(2)O (30/5, 50 degrees C/5 min, resp.), 1 g catalyst/30 g acetone. At 35 kHz, a power d. as low as 0.092 W/g acetone was also effective. Over other alk. catalysts (NaOH, KOH, CaO, LiOH.H2O, KOH (or KF)/Al2O3), equil. conversion (9.1%) was attained in as few as 5-10 min. Microwaves (2.45 GHz from a 3-GHz, 250W, 1-100 bar reactor) used in conjunction with any of nine alk. catalysts (or catalyst systems) examd., gave rise to advanced condensates or even oligomers. Over the alk. and the acid catalysts used, isophorone and mesitylene were the major products, resp. Theoret. modeling bore out low temps. and high pressures to favor selective formation of DAA. 50 refs.