  We consider the compressive wave for the modified Korteweg--de Vries equation
with background constants $c>0$ for $x\to-\infty$ and $0$ for $x\to+\infty.$ We
study the asymptotics of solutions in the transition zone $4c^2t-\varepsilon
t<x<4c^2t-\beta t^{\sigma}\ln t$ for $\varepsilon>0,$ $\sigma\in(0,1),$
$\beta>0.$ In this region we have a bulk of nonvanishing oscillations, the
number of which grows as $\frac{\varepsilon t}{\ln t}.$ Also we show how to
obtain Khruslov--Kotlyarov's asymptotics in the domain $4c^2t-\rho\ln
t<x<4c^2t$ with the help of parametrices constructed out of Laguerre
polynomials in the corresponding Riemann-Hilbert problem.
