  In this paper, we revisit large variable asymptotic expansions of tronqu\'ee
solutions of the Painlev\'e I equation, obtained via the Riemann-Hilbert
approach and the method of steepest descent. The explicit construction of an
extra local parametrix around the recessive stationary point of the phase
function, in terms of complementary error functions, makes it possible to give
detailed information about non-perturbative contributions beyond standard
Poincar\'e expansions for tronqu\'ee and tritronqu\'ee solutions.

Classical Analysis and ODEs;Complex Variables