  Classical (It\^o diffusions) stochastic volatility models are not able to
capture the steepness of small-maturity implied volatility smiles. Jumps, in
particular exponential L\'evy and affine models, which exhibit small-maturity
exploding smiles, have historically been proposed to remedy this (see
\cite{Tank} for an overview), and more recently rough volatility models
\cite{AlosLeon, Fukasawa}. We suggest here a different route, randomising the
Black-Scholes variance by a CEV-generated distribution, which allows us to
modulate the rate of explosion (through the CEV exponent) of the implied
volatility for small maturities. The range of rates includes behaviours similar
to exponential L\'evy models and fractional stochastic volatility models.
