Limiting computation

I would like to run a limited groebner basis-type algorithm, where whenever an S-polynomial is generated it is discarded if it does not satisfy some property (typically the total degree of the leading term is higher than some constant).

Is this possible in Singular?

Currently, you cannot specify arbitrary conditions for that,
but in this case degBound may help
(see http://www.singular.uni-kl.de/Manual/3-0-2/sing_325.htm)