MELIBEA is a Spanish database that uses a composite formula with eight weighted conditions to estimate the effectiveness of Open Access mandates (registered in ROARMAP). We analyzed 68 mandated institutions for publication years 2011-2013 to determine how well the MELIBEA score and its individual conditions predict what percentage of published articles indexed by Web of Knowledge is deposited in each institution's OA repository, and when. We found a small but significant positive correlation (0.18) between MELIBEA score and deposit percentage. We also found that for three of the eight MELIBEA conditions (deposit timing, internal use, and opt-outs), one value of each was strongly associated with deposit percentage or deposit latency (immediate deposit required, deposit required for performance evaluation, unconditional opt-out allowed for the OA requirement but no opt-out for deposit requirement). When we updated the initial values and weights of the MELIBEA formula for mandate effectiveness to reflect the empirical association we had found, the score's predictive power doubled (.36). There are not yet enough OA mandates to test further mandate conditions that might contribute to mandate effectiveness, but these findings already suggest that it would be useful for future mandates to adopt these three conditions so as to maximize their effectiveness, and thereby the growth of OA.