  A closed interval and circle are the only smooth Julia sets in polynomial
dynamics. D. Ruelle proved that the Hausdorff dimension of unicritical Julia
sets close to the circle depends analytically on the parameter. Near the tip of
the Mandelbrot set M, the Hausdorff dimension is generally discontinuous.
Answering a question of J-C. Yoccoz in the conformal setting, we observe that
the Hausdorff dimension of quadratic Julia sets depends continuously on $c$ and
find explicit bounds at the tip of M for most real parameters in the the sense
of 1-dimensional Lebesgue measure.
