When designing a digital filter based on an analog filter we usually use the [bilinear transform](http://en.wikipedia.org/wiki/Bilinear_transform). To approximate a discrete transfer function $D\_a(z)$ from analog (continuous) transfer function $A(s)$ we substitute 

$$z = \frac{1+sT/2}{1-sT/2}$$

where $T$ is the sampling period. Alternatively, to approximate an continuous transfer function $A\_a(s)$ from discrete transfer function $D(z)$ we substitute

$$s = \frac{2}{T} \frac{z-1}{z+1}$$

Are there alternative methods of performing such conversions? Are there better approximations?