Standard asymptotic descriptions of stellar p-modes use 1/ω as a small parameter; either the degree ℓ is kept constant in the asymptotic expansions (e.g. Tassoul 1980), or the parameter , which specifies the position of the inner turning point (e.g. Vorontsov 1991). At low degree, due to the strong effects of gravity perturbations, these expansions are known to produce rather poor results, even when developed to higher order (Roxburgh and Vorontsov 1994). Here, we employ an alternative asymptotic expansion, capable of providing much better accuracy at low degree-with as a small parameter instead of 1/ω, and test its diagnostic capabilities.