Research groups spend time and resources in the process of applying for funding. This issue raises important questions regarding inefficiency and whether the currently used funding mechanisms are adequate. This article aims to identify ways of reducing the inefficiency and the waste of resources when making research funding calls. We look at four ways of reducing inefficiency. Inefficiency decreases when: (1) the most productive research groups are favoured over the less productive ones, (2) the call is restricted to a small number of research groups actively working on the subject of the call, (3) the funding process is less dependent on the amount of effort spent on fund-seeking activities by the research groups, and (4) the number of research groups competing in the same call is small. However, not all these mechanisms are equally powerful or easy to implement. Our results suggest that: (1) reducing the dependence of the funding process on funding activities' efforts; or (2) reducing the number of research groups by narrowing the subject of the call to groups that are very active in the call's subject might be particularly effective in reducing inefficiency.