The complexity of medical problems is a well-recognized phenomenon. In the presence of economic and cultural restrictions, medical decision-making can be particularly challenging. This paper outlines a system of analysis and decision-making for solving such problems, and briefly describes a case study in which the method was used to analyze the case of antibiotic overprescribing in a large health maintenance organization. The purpose of the study was to determine if a technique for problem-solving in the field of engineering could be applied to the complex problems facing primary care. The method is designated Systematic Inventive Thinking and consists of a three-step procedure: problem reformulation, general search-strategy selection, and an application of idea-provoking techniques. The problem examined is the over-prescribing of antibiotics by general practitioners working in Maccabi Healthcare Services, an HMO serving one and a half million patients in Israel. The group of healthcare professionals involved in the discussions generated 117 ideas for improving antibiotic use. Six of these ideas were then implemented in a national campaign in the winter of 2000/1 and 2001/2. During this period, a significant reduction in per-visit antibiotic purchasing was observed for influenza visits (from 79.2 per 1,000 to 58.1 per 1,000, P < 0.0001), but not for other categories of visits. The SIT methodology is a useful technique for problem-solving and idea generation within the medical framework.