AbstractGroup sequential monitoring is used to provide guidance on stopping a clinical trial in progress based on interim evaluation of its efficacy objectives. A trial could stop because an experimental regimen (1) is efficacious, (2) lacks any sign of efficacy, or (3) is specifically less efficacious than a control. Group sequential methods using α‐ and β‐spending functions (Biometrika 1983; 70:659–663) are often used to create stopping boundaries for test statistics for efficacy hypotheses computed at interim analyses. This paper explores fitting α‐ and β‐spending functions that have specific values at specific interim analyses. Commonly used one‐parameter families may not provide an adequate fit to more than one desired critical value. We define new one‐ and two‐parameter families to provide additional flexibility along with examples to demonstrate their usefulness. The logistic family is one of these two‐parameter families, which has been applied in several trials. Copyright © 2009 John Wiley & Sons, Ltd.