  For $k=1,2$, let $f_k=h_k+\overline{g_k}$ be normalized harmonic right
half-plane or vertical strip mappings. We consider the convex combination
$\hat{f}=\eta f_1+(1-\eta)f_2 =\eta h_1+(1-\eta)h_2 +\overline{\overline{\eta}
g_1+(1-\overline{\eta})g_2}$ and the combination $\tilde{f}=\eta
h_1+(1-\eta)h_2+\overline{\eta g_1+(1-\eta)g_2}$. For real $\eta$, the two
mappings $\hat{f}$ and $\tilde{f}$ are the same. We investigate the univalence
and directional convexity of $\hat{f}$ and $\tilde{f}$ for $\eta\in\mathbb{C}$.
Some sufficient conditions are found for convexity of the combination
$\tilde{f}$.
