An analysis of alpha-particle containment in tokamaks is presented. It is found that, for the relatively peaked profiles and low aspect ratio of the present devices, the contained fraction F depends mainly on the product IA of plasma current and aspect ratio, the dependence on other parameters being weak. When the effect of the magnetic-field ripple on the trajectories is considered, the increase of F with IA becomes weak for IA > 5 MA and IA tends to saturate at F ≅ 0.9. This indicates that, for relatively peaked profiles in the presence of ripple, there is only a weak improvement in alpha-particle confinement by increasing the plasma current above about 2 MA.