  Using samples of (5.93 +/- 0.10) x 10^6 Upsilon(3S) decays and (9.11 +/-
0.14) x 10^6 Upsilon(2S) decays collected with the CLEO detector, we report
improved measurements of the branching fractions for the following five
transitions: B(Upsilon(3S)-->Upsilon(1S) pi^+ pi^-) = (4.46 +/- 0.01 +/-
0.13)%, B(Upsilon(2S)-->Upsilon(1S) pi^+ pi^-) = (18.02 +/- 0.02 +/- 0.61)%,
B(Upsilon(3S)-->Upsilon(1S) pi^0 pi^0) = (2.24 +/- 0.09 +/- 0.11)%,
B(Upsilon(2S)-->Upsilon(1S) pi^0 pi^0) = (8.43 +/- 0.16 +/- 0.42)% and
B(Upsilon(3S)-->Upsilon(2S) pi^0 pi^0) = (1.82 +/- 0.09 +/- 0.12)%. In each
case the first uncertainty reported is statistical, while the second is
systematic.
