We present results from 170ksec long RXTE observations of LMC X-1 and LMC X-3, taken in 1996 December, where their spectra can be described by a disc black body plus an additional soft (Gamma~2.8) high-energy power-law (detected up to 50keV in LMC X-3). These observations, as well as archival ASCA observations, constrain any narrow Fe line present in the spectra to have an equivalent width 0.2Hz, possibly indicating an outer disc radius of ~1000GM/c^2 in this likely wind-fed system. Furthermore, the coherence function between variability in the > 5keV band and variablity in the lower energy bands is extremely low. We discuss the implications of these observations for the mechanisms.