Low Mass X-Ray Binaries (LMXBs) are astrophysical systems in which a black hole or neutron star accretes matter from a stellar companion. Accreting matter forms a disk around the compact object, within which temperatures reach millions of Kelvin. Internal radiation pressure generated by this heating places a theoretical upper limit on the accretion rate, known as the Eddington Limit. Several LMXBs are known to accrete at close to, or even above, their Eddington Limits; models of accretion disks suggest we should expect large-scale instabilities in the inner accretion disk in this radiation- dominated regime. Indeed in the black hole LMXB GRS 1915+105, known to accrete at >80% of its Eddington Limit, X-Ray lightcurves reveal a rich array of different types of second-to-minute scale variability; this ranges from quasiperiodic flares to irregular dips in flux. GRS 1915-like variability has also been seen in two additional LMXBs, the Black Hole Candidate IGR J17091-3624 and the neutron star system known as the 'Rapid Burster'. However, the Rapid Burster is known to be accrete at less than 20% of its Eddington Limit, while sources such as the neutron star GRO J1655-40 have been observed accreting close to Eddington without showing GRS 1915-like variability. Consequently, our understanding of this phenomenology as driven by radiation-pressure-driven instability is called into question. In this talk I will summarize the results of a detailed study of IGR J17091-3624 and how it compares with GRS 1915 and I will discuss their implications to our understanding of radiation- dominated accretion physics.