Convective overshooting increases the fraction of the star which is ef
fectively mixed, thus altering models of stellar evolution. If the fee
d back of overshooting on the structure of the star is neglected the e
stimated extent of overshooting is very small. If the feed back is inc
luded in these estimates then the adiabatic core is extended by a dist
ance comparable to a substantial fraction of the radius of the unstabl
e region. An upper limit on convective overshooting is given by the in
tegral constraint (Roxburgh 1978,1989) with viscous dissipation neglec
ted. If this constraint is applied to small convective cores then the
maximum extent of the penetration region is shown to be at most about
0.18 times the radius of the core independent of the details of energy
generation and opacity. The ratio of the maximum penetration distance
to the scale height at the edge of the ''classical boundary'' varies
very strongly with core size, and modelling overshooting by taking the
penetration distance as a multiple of the scale height is likely to g
ive misleading results. Numerical simulations of two-dimensional compr
essible convection in a fluid where the central regions are naturally
convectively unstable, and the surrounding layers are stable, have bee
n undertaken for different values of the Prandtl number. The results i
ndicate that for low Prandtl numbers viscous dissipation is of decreas
ing importance and the simple integral condition gives a reasonable es
timate of the extent of overshooting. Stellar seismology offers the po
ssibility of detecting the location of the core - envelope interface t
hrough a periodic variation of the small frequency separation with