We demonstrate broadband supercontinuum generation over two infrared octaves, spanning from 1.3 to 5.3 μm, with an output power of 150 mW in robust step-index tellurite fibers with core diameters between 3.5 and 4.3 μm. As a pump source, we use femtosecond mid-IR pulses from a home-built post-amplified optical parametric oscillator tunable between 1.5 and 4.0 μm at a 43 MHz repetition rate. We study the influence of core size, pump wavelength, and fiber length to optimize the spectral bandwidth. A key requirement for efficient spectral broadening is a low and rather flat average anomalous dispersion over a wide spectral range that can be tailored accordingly by changing the fiber core diameter. Numerical simulations based on the generalized nonlinear Schrödinger equation are in good agreement with experimental results.