<p>The best integer equivariant (BIE) estimator takes advantage of the integer nature of the ambiguities, resulting in a solution that is always superior to the integer estimator and least-squares estimator in the criterion of the mean-square error (MSE). In precise point positioning (PPP), the BIE estimator can shorten the convergence time and improve the positioning precision. Recently, research on GNSS observations under elliptically contoured distributions (ECDs) has become a popular topic. The framework of the BIE theory is established, with explicit expressions of the BIE estimator for the normal, contaminated normal, and <i>t</i> distributions being given. The BIE estimator under the contaminated normal and <i>t</i> distributions is derived from the distribution of the original observation data. In this contribution, a BIE estimator within a more restricted class is introduced. It is obtained by applying Teunissen’s BIE-ECDs theory to the least-squares estimator of integer ambiguity rather than to the original observed data. As a result, the “best” property holds true only within a more restricted IE class. The advantages and suboptimality of the “restricted BIE” under the contaminant normal and <i>t</i> distributions are validated via simulation data, as well as real GNSS-observed data. Both of them show that the “restricted BIE” solutions are MSEs superior to the ILS solutions and slightly inferior to the BIE solutions.</p>