To fully utilize carrier phase measurements in high-precision interferometric positioning systems, such as global navigation satellite systems (GNSS), the corresponding integer ambiguities must be successfully resolved. Since the phase ambiguities are biased by non-integer phase delays, only specific combinations are allowed to serve as valid inputs for Integer Ambiguity Resolution (IAR) methods. Consequently, the resultant ambiguity-resolved phase data may not improve position precision as significantly as when all the ambiguities are resolved. The goal of this contribution is to study the role of phase biases in IAR and quantify the effect of bounding such biases in the ambiguity-resolved positioning performance. By identifying the interrelationship of the model's solutions, we show how constraining the phase biases has the potential to improve the precision of both the position and the ambiguities. With the aid of simulated results, it is illustrated that one can leverage the boundedness property of phase biases to obtain positioning results that are considerably more accurate than those obtained when the bias constraint is discarded.