It is prohibitively expensive to deposit customized dielectric coatings on individual optics. One solution is to batch-coat many optics with extra dielectric layers, then remove layers from individual optics as needed. Here we present a low-cost, single-step, monitored wet etch technique for reliably removing individual SiO2 and Ta2O5 dielectric layers, in this case from a high-reflectivity fiber mirror. By immersing in acid and monitoring off-band reflected light, we show it is straightforward to iteratively (or continuously) remove six bilayers. At each stage, we characterize the coating performance with a Fabry-Pérot cavity, observing the expected stepwise decrease in finesse from 92,000 ± 3,000 to 3, 950 ± 50, finding no evidence of added optical losses. The etch also removes the fiber's sidewall coating after a single bilayer, and, after six bilayers, confines the remaining coating to a 60-µm-diameter pedestal at the center of the fiber tip. Vapor etching above the solution produces a tapered "pool cue" cladding profile, reducing the fiber diameter (nominally 125 µm) to 95 µm at an angle of ∼0.3° near the tip. Finally, we note that the data generated by this technique provides a sensitive estimate of the layers' optical depths. This technique could be readily adapted to free-space optics and other coatings.