Minimum-wage legislation is less likely to have adverse effects on employment when the

labor market is monopsonistic.

Explanation:

A monopsonistic labor market is a market were only one dominant employer exists. In this case, the employer has total leverage in determining the wages he will offer and as you can guess they are probably very low. In order to balance the situation, a minimum wage can be set in order to limit the power of the monopsonistic employer.

This situation usually happens on small populations, for example a town that relies almost completely on a huge factory or a huge mine that employs most of the workers that live in the town. Sometimes factories get so big that they can become natural monopsonies, like Toyota City in Japan.