A weakness for drink is only one of the problems encountered by the Native American characters in Sydney Freeland’s debut feature, “Drunktown’s Finest.”

Sick Boy (Jeremiah Bitsui) becomes violent when drunk and keeps failing his pregnant wife and the sergeant recruiting him for basic training. The transgender Felixia (Carmen Moore) has low self-esteem and falls for men who pay her for her time. And a college student, Nizhoni (MorningStar Angeline), is an adoptee who feels the ache of missing her birth parents.

These stories migrate between the worlds of a drive-through New Mexico town and a nearby Navajo reservation. (The film’s title comes from a “20/20” report about Ms. Freeland’s hometown, Gallup, N.M., that understandably still carries a sting.) The screenplay tracing the characters’ struggles has a tidy, workshopped feel, and the dialogue and acting can be gratingly flat. But what gives the film a certain confidence is its cultural specificity and the fresh clashes and contrasts it presents.