Markov-recapture population size estimates rely on insects (or other animals) marking themselves before arrival in a trap. Assumptions about rates of marking and capture are based upon the sampling scheme, and the estimate is based on the resulting multinomial probability distribution. The original scheme used one marking station per trap, yielding an assumption of equal rates of marking and capture. This paper explores more general schemes that provide better resolution, sometimes with added degrees of freedom, and which provide estimates more quickly than the original scheme (reducing the risk of violating assumptions). The alternative schemes involve varying the ratio of marking stations to traps and multiple marking. The paper continues to describe the maximum likelihood estimates of population size based on these sampling schemes and gives a rough correction for the bias of the population estimate, found by using a jackknife technique. Two standard error confidence limits are explicit expressions obtained using asymptotic maximum likelihood arguments; these work well in conjunction with the corrected estimate if trapping has continued for an extended period. Relative likelihood-based confidence intervals perform better than two standard error intervals over a wide range of parameter values, especially where trapping has not continued for an extended period. The method tends to become biased when used in an open or growing population. Goodness-of-fit tests are possible with the added degrees of freedom but are not very powerful.