We report on searches for B0(s) --> mu+ mu-, B0(d) -->
mu+ mu- decays and b --> s mu+ mu- transitions in exclusive decays of
B mesons.  Using 2 fb-1 of data collected by the CDF II detector we find
upper limits on the branching fractions B(B0(s) --> mu+ mu-) < 5.8 x
10-8 and B(B0(d) --> mu+ mu-) < 1.8 x 10-8 at 95% confidence level.
Using 924 pb-1 of data we measure the branching fractions B(B+ -->
mu+ mu- K+) = (0.60 +/- 0.15 +/- 0.04) x 10-6, B(B0(d) --> mu+ mu-
K*0) = (0.82 +/- 0.31 +/- 0.10) x 10-6 and the limit B(B0(s) --> mu+
mu- phi)/B(B0(s) --> J/psi phi) < 2.61(2.30) x 10-3 at 95(90)%
confidence level.