We measure a cold collision frequency shift in an 87Rb fountain clock that is fractionally 30 times smaller than that for Cs. The shift is -0.38(8) mHz for a density of 1.0(6)x10(9) cm(-3). We study the cavity pulling of the atomic transition and use it to cancel the cold collision shift. We also measure the partial frequency shifts of each clock state finding 2(lambda(10)-lambda(20))/(lambda(10)+lambda(20)) = 0.1(6).