In order to test ab initio calculations of light nuclei, we have remeasured lifetimes in Be10 using the Doppler shift attenuation method (DSAM) following the Li7(Li7,α)Be10 reaction at 8 and 10 MeV. The new experiments significantly reduce systematic uncertainties in the DSAM technique. The Jπ=21+ state at 3.37 MeV has τ=205±(5)stat±(7)sysfs corresponding to a B(E2) of 9.2(3)e2fm4 in broad agreement with many calculations. The Jπ=22+ state at 5.96 MeV was found to have a B(E2) of 0.11(2)e2fm4 and provides a more discriminating test of nuclear models. New Green's function Monte Carlo calculations for these states and transitions with a number of Hamiltonians are also reported and compared to experiment