We introduce two new regression methods (based on radial basis functions and tensors of radial basis functions) to the least-squares Monte Carlo method in the context of gas storage valuation with the spot approach. Furthermore, we propose a new methodology that combines two existing ones in the spot approach: discretization of volume with multivariate regressions. Our numerical examples show that these new valuation methods match and frequently manage to exceed the value of our benchmark. We also find that the valuation suffers in the case where insufficient points are placed near the volume boundaries. We expect that our new methodology, in combination with the two new regression methods, will prove beneficial in solving valuation problems with several price factors and volume levels in the future.