New Mexico's 19 "very small" school districts (fewer than 300 average daily membership K-12 in 1981-82) were studied to identify major problems (including program deficiencies and actions being taken to alleviate those problems), to determine appropriate additional measures which might be helpful in resolving the problems, and to ascertain whether adjustments in the funding formula would substantially alleviate any of the problems. Although very small districts are largely ignored in the literature, the 19 very small districts represent 21% of New Mexico's school districts. Data were obtained from a questionnaire sent to the superintendents, from a meeting of representatives from 10 of the smallest districts, and from information from the public school finance division and the state department of education. The four primary concerns of the school districts were: certification, multiple endorsement, and staff development; adequate instructional programs and student services; salary comparability; and housing and community resources. There are some things that can be done (some examples are given) within individual districts, among districts, and in conjunction with nearby postsecondary schools to alleviate many of the problems. The encouragement and leadership of state regulatory and funding agencies, the Legislature, and state professional organizations are also needed. (BRR)