We present alternative source models for very low frequency (VLF) events, previously inferred to be radiation from individual slow earthquakes that partly fill the period range between slow slip events lasting thousands of seconds and low-frequency earthquakes (LFE) with durations of tenths of a second. We show that VLF events may emerge from bandpass filtering a sum of clustered, shorter duration, LFE signals, believed to be the components of tectonic tremor. Most published studies show VLF events occurring concurrently with tremor bursts and LFE signals. Our analysis of continuous data from Costa Rica detected VLF events only when tremor was also occurring, which was only 7% of the total time examined. Using analytic and synthetic models, we show that a cluster of LFE signals produces the distinguishing characteristics of VLF events, which may be determined by the cluster envelope. The envelope may be diagnostic of a single, dynamic, slowly slipping event that propagates coherently over kilometers or represents a narrowly band-passed version of nearly simultaneous arrivals of radiation from slip on multiple higher stress drop and/or faster propagating slip patches with dimensions of tens of meters (i.e., LFE sources). Temporally clustered LFE sources may be triggered by single or multiple distinct aseismic slip events or represent the nearly simultaneous chance occurrence of background LFEs. Given the nonuniqueness in possible source durations, we suggest it is premature to draw conclusions about VLF event sources or how they scale.