 An alternative approach to contraction of belief bases has been proposed under the name kernel contraction. For any sentence \(p\), a \(p\)-kernel is a minimal \(p\)-implying set, i.e. a set that implies \(p\) but has no proper subset that implies \(p\). A contraction operation \(\div\) can be based on the simple principle that no \(p\)-kernel should be included in \(A\div p\). This can be obtained with an incision function, a function that selects at least one element from each \(p\)-kernel for removal. An operation that removes exactly those elements that are selected for removal by an incision function is called a kernel contraction. It turns out that all partial meet contractions on belief bases are kernel contractions, but some kernel contractions are not partial meet contractions. In other words, kernel contraction is a generalization of partial meet contraction.