Using data accumulated with the CLEO detector corresponding to an integrated luminosity of [symbol: see text] = 5.63 pb(-1) on the peak of the psi(2S) [3.08 x 10(6) psi(2S) decays] and 20.70 pb(-1) at square root of[s] = 3.67 GeV, we report first measurements of the branching fractions for the following 13 decay modes of the psi(2S): eta3pi, &eta'3pi, rhoK+K-, K+K-pi+pi-pi0, 2(K+K-), 2(K+K-)pi0, rhopp, pppi+pi-pi0, etapp, ppK+K-, lambdalambdapi+pi-, lambdapK+, and lambdapK+pi+pi-, and more precise measurements of 8 previously measured modes: 2(pi+pi-), rhopi+pi-, 2(pi+pi-)pi0, omegapi+pi-, K+K-pi+pi-, omegaK+K-, phiK+K-, and pppi+pi-. We also report new branching fraction measurements of phipi+pi- and omegapp and upper limits for etapi+pi-, etaK+K-, and phivpp. Results are compared, where possible, with the corresponding J/psi branching ratios to provide new tests of the 12% rule.