We have re-analysed models of the breakdown of dioecy involving modified males, to investigate female frequencies in the resulting gynodioecious populations. We extend and simplify previous treatments to deal with biologically relevant factors including pollen limitation, partial selfing of modified males, and inbreeding depression, to highlight the different empirically detectable advantages that may be gained by modified males that can reproduce as cosexes (i.e. can produce some seeds); these include "inconstant males", which can sometimes display some female function. Males reproducing wholly or occasionally as cosexual phenotypes can gain the transmission advantage of selfing, if partial self-fertilisation is possible, and from reproductive assurance when pollen is limiting. If, due to resource limitation, such cosexual phenotypes produce fewer ovules than females, their non-selfed ovules will require a lower pollen pool size for full seed-set, compared with females. We investigate the conditions for these benefits to allow modified males to invade dioecious populations. Sometimes, such invasion leads to replacement of dioecy by the cosexual type, but sometimes the breakdown populations remain sexually polymorphic. When competition occurs between genotypes in the pollen load on a flower, high female frequencies can arise when Y chromosome-bearing pollen competes poorly with X pollen. This article is protected by copyright. All rights reserved.