In this paper, the authors study issues of continuous extension to \(\overline{\mathbb{D}}\), uniqueness of (normalized) extremal mappings, and quasiconformal extensions to the entire plane of functions defined in the unit disk \(\mathbb{D}\) satisfying \[ Sf(z)\leq\frac{4t}{1-| z| ^2}, \quad t\leq 1. \tag{1} \] Here \(Sf\) is the Schwarzian derivative. When \(t=1\) then (1) corresponds to one of many sufficient conditions for univalence in \(\mathbb{D}\), announced originally by \textit{V. V. Pokornyi} [Dokl. Akad. Nauk SSSR 79, 743--746 (1951; Zbl 0045.35901)] (in Russian) and established by \textit{Z. Nehari} [Proc. Am. Math. Soc. 5, 700--704 (1954; Zbl 0057.31102)]. When \(t<1\) then condition (1) guarantees the existence of a quasiconformal extension of \(f\) to the plane. Most of the results in this paper are already known.