I just tried out the quota “Least Filled” Feature in Lighthouse Studio v9.7 (soon to be released) and it worked very well! I wanted to randomize respondents into six cells with target sample sizes of 50, 50, 50, 50, 100, and 100. I fielded the study using MTurk yesterday and achieved sample sizes of 51, 50, 50, 50, 100, and 100. This gives much tighter control than the previous approach that assigned respondents randomly according to target probabilities per quota cell, but due to the variability in random draws didn’t offer nearly as tight of control to target sample sizes that this new feature offers.
Because you don’t know for certain whether a respondent who begins the survey will finish it and you don’t want to terminate a respondent who starts the survey due to quota overfill, you cannot always achieve exactly the quotas you target. This new feature scheduled for release in the next month in v9.7 gets you much closer than before when randomizing respondents across cells (a needed approach for certain survey experiments you may wish to conduct).