Some X-ray bursts from sources such as 4U/MXB 1636-53, 4U 1608-52, and possibly MXB 1728-34, display a multipeaked structure in the bolometric flux that is difficult to reconcile with the standard thermonuclear flash model or with the effects due to photospheric expansion and contraction. Understanding this phenomenon is important primarily because it might be due to a variable Thomson optical depth along a line of sight threading the burst-induced accretion disk corona. As such, multipeaked bursts offer us some hope of learning more about the still poorly understood accretion disk geometry in these systems. Here, we explore the conditions under which these burst profiles might be observed, in light of the somewhat surprising recent results from the radiative-hydrodynamic simulation of the coronal structure. We find that double- (and triple-) peaked bursts are produced at inclination angles 40-degrees less than or similar to i less than or similar to 65-degrees. Interestingly, the orbital information for 4U/MXB 1636-53 and 4U 1608-52 suggests i < 70-degrees, in these sources. The orbital inclination of MXB 1728-34 is not yet known.