  We extend the scope of B. Shapirovskii's results [B.E Shapirovskii, "Cardinal
invariants in Compact Hausdorff Spaces," Amer. Math. Soc. Transl. (2) Vol. 134,
1987, pp. 93-118] on the order of $\pi$-bases in compact spaces and answer some
questions of V. Tkachuk in [V.V. Tkachuk, "Point-countable pi-bases in
first-countable and similar spaces," Fund. Math. 186 (2005), pp.55-69].
