<p>A sensitivity study was performed on method-blank samples for alpha spectrometry. The samples of water, analyzed for ²³⁹Pu and U-nat (²³⁴U, ²³⁵U, ²³⁸U) isotopes, were spiked with the ²³⁶Pu and ²³²U isotope-dilution tracers. The effects of various methods of uncertainty propagation and corrections were studied. In addition, classical detection limits were calculated in terms of decision level, detection limit, upper limit, and determination limit. Cases of zero counts were compared with the Bayesian theory of zero-count detector. Also, detection limits according to the Safe Drinking Water Act definition were calculated. Using the proposed continuity correction, a 4.7% of false-positive rates was observed. The average minimum detectable activities calculated were 0.61, 0.81, 0.82, and 0.74&#xa0;mBq L⁻¹ for ²³⁹Pu, ²³⁴U, ²³⁵U, and ²³⁸U, respectively.</p>