Stable water isotopes in ice cores serve as a valuable proxy for the climate of the past hundreds of thousands of years. Over time, water isotope diffusion causes significant attenuation of the isotopic signal, exacerbated in deep ice due to extreme layer thinning and increased temperatures from geothermal heat flux. This damping affects higher frequencies to a greater extent, erasing information on the shortest timescales. It is possible to restore some of the attenuated variability through deconvolution, a method which reverses the effect of diffusion. However, since the measured isotopic signal always contains noise from the measurement process, deconvolution inevitably amplifies this measurement noise along with the isotopic signal. Thus the effectiveness of deconvolution depends on the precision of the measurements, with noisier data limiting the ability to restore otherwise resolvable frequencies. Here, we quantify the upper frequency limit introduced by the magnitude of the measurement noise analytically for different climate states, and offer a numerical example using the Beyond EPICA Oldest Ice Core (BE-OIC). We also demonstrate the qualitative significance of measurement noise on simulated Antarctic isotopic profiles. The general resolution improvement for firn or upper ice records is on the order of 1.5 times for a 10-fold reduction in measurement noise. Similarly, throughout the BE-OIC, we find the deconvolution of <em>δ</em><sup>18</sup>O records with measurement error of 0.1 ‰ contributes a 1.5 times increase in the maximum resolvable frequency, which rises to a factor of 2 improvement after reducing the measurement noise to 0.01 ‰. While progress is continuously being made towards improving precision of stable isotope measurements, further improvements using longer integration times should be considered when analysing limited and precious deep ice in order to obtain the most faithful climate reconstructions possible.