‎In this paper‎, ‎under certain conditions‎, ‎the usual stochastic‎, ‎convex and dispersive orders between the smallest claim amounts with independent Weibull claims are discussed‎. ‎Also‎, ‎under conditions on some well-known common copula‎, ‎some stochastic comparisons of smallest claim amounts with dependent heterogeneous claims have been obtained‎.