The paper exhibits three results on quasivarieties of (distributive) \(p\)- algebras: There exists a quasivariety \(\mathbb{K}\) of such algebras such that \(\mathbb{B}_ 2\subset\mathbb{K}\subset\mathbb{B}_ 4\), but neither \(\mathbb{K}\subseteq\mathbb{B}_ 3\) nor \(\mathbb{B}_ 3\subseteq\mathbb{K}\), where \(\mathbb{B}_ i\) denotes the \(i\)-th Lee class. This disproves a conjecture of Pigozzi (``any quasivariety of \(p\)- algebras lies between two consecutive Lee classes''). If \(\mathbb{K}\) is a quasivariety of \(p\)-algebras such that for each \(A\in\mathbb{K}\) the lattice of all \(\theta\in\text{Con}(A)\) with \(A/\theta\in\mathbb{K}\) is distributive, then \(\mathbb{K}\) is actually a variety. If \(\mathbb{K}\) is a quasivariety of \(p\)-algebras such that for every \(A,B\in\mathbb{K}\) and \(\theta\in\text{Con}(A)\) with \(A\triangleleft B\) and \(A/\theta\in\mathbb{K}\) there exists \(\varphi\in\text{Con}(B)\) with \(B/\varphi\in\mathbb{K}\) and \(\theta=(A\times A)\cap\varphi\), then \(\mathbb{K}\) is actually a variety. The proof of the first result relies on Priestley duality for distributive \(p\)-algebras, while the other two are based on results of Czelakowski and Dziobiak.