All-fiber-optic imaging microendoscopes are emerging as an important tool in bioimaging studies, but physical limitations constrain the achievable beam characteristics of designs using a single focusing element. These constraints are especially relevant for applications that require a long working distance, high resolution, and/or minimal probe diameter. Through detailed analysis based on ABCD matrix modelling, we show that side-viewing probes combining a graded-index fiber (GRIN) with a ball lens -GRIN-ball-lens probes (GBLPs) -offer superior performance over a range of numerical apertures and pave the way for a broader range of imaging applications. The performance of side-viewing GBPLs designed for 1300-nm optical coherence tomography imaging is compared against commonly used single-focusing-element all-fiber side-viewing probe designs, namely, ball-lens probes (BLPs) and GRIN-fiber probes (GFPs). All possible realizations of this novel probe design and their impact on the requisite design tradeoffs are investigated, including the impact on probe performance of fabrication error and the refractive index of the surrounding medium. Applications of GBLPs, including ultra-high-resolution (sub-2 micrometer) miniature probes for micro-endomicroscopy, are discussed.