A trigger-actuated atomizer pump has a first engagement member held in fitting engagement with a second engagement member on a flattened liquid container for orienting the atomizer pump securely against rotation relative to the flattened liquid container with an atomizer trigger directed in registration with the plane in which the container is flattened. The first engagement member may include a lateral projection extending remotely from the atomizer trigger so that an operator's hand can be held at the back of the thenar against the lateral projection to facilitate gripping the atomizer for fatigue-free operation in a long period of time.