Using the recently introduced method to calculate bubble abundances in an eternally inflating spacetime, we investigate the volume distribution for the cosmological constant $Lambda$ in the context of the Bousso-Polchinski landscape model. We find that the resulting distribution has a staggered appearance which is in sharp contrast to the heuristically expected flat distribution. Previous successful predictions for the observed value of $Lambda$ have hinged on the assumption of a flat volume distribution. To reconcile our staggered distribution with observations for $Lambda$, the BP model would have to produce a huge number of vacua in the anthropic range $DeltaLambda_A$ of $Lambda$, so that the distribution could conceivably become smooth after averaging over some suitable scale $deltaLambdallDeltaLambda_A$.
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