  A direct relation between the conformal formalism for 2d-quantum gravity and
the W-constrained KP hierarchy is found, without the need to invoke
intermediate matrix model technology. The Kontsevich-Miwa transform of the KP
hierarchy is used to establish an identification between W constraints on the
KP tau function and decoupling equations corresponding to Virasoro null
vectors. The Kontsevich-Miwa transform maps the $W^{(l)}$-constrained KP
hierarchy to the $(p^\prime,p)$ minimal model, with the tau function being
given by the correlator of a product of (dressed) $(l,1)$ (or $(1,l)$)
operators, provided the Miwa parameter $n_i$ and the free parameter (an
abstract $bc$ spin) present in the constraints are expressed through the ratio
$p^\prime/p$ and the level $l$.
