  Roughly 30% of variable AGB stars show a Long Secondary Period, or LSP. These
LSPs have posed something of a problem in recent years and their cause remains
a mystery. By combining VLT-derived velocity curves with MACHO and OGLE light
curves we were able to examine many properties of these stars and test the
theory that LSPs are caused by binarity. We show why we concluded that the
binary model for LSPs is unlikely. Examining mid-infrared SAGE observations for
stars with LSPs shows that these stars are surrounded by a significant amount
of cool dust in a nonspherical distribution, e.g. a disk or clumps. The
unlikeliness of binarity in these stars forces us to conclude that the dust is
not in a disk. We are left without an acceptable explanation for Long Secondary
Periods in AGB stars.
