Latin hypercube designs are frequently used in estimating the mean output value of computer simulations given random environmental factors. Sliced Latin hypercube designs are designs that can be partitioned into a number of batches so that both the whole design and the batches achieve optimal univariate uniformity. Such designs are useful for computer simulations that are carried out in batches, come from multiple resources or have categorical variables. Most existing sliced Latin hypercube designs have equal batch sizes. Firstly, we propose a new type of sliced Latin hypercube design that has unequal batch sizes based on randomly Latin hypercube designs. We show its advantages theoretically and numerically. Secondly, based on midpoint Latin hypercube designs, we give, to the best of our knowledge, the first construction of sliced Latin hypercube designs that allow arbitrarily chosen run sizes for the slices. We also provide an algorithm to reduce correlations of our proposed designs.