For smooth \(C^\infty\) manifolds \(N^n\) and \(M^m\), \(n\ge m\), a smooth map germ \(f:(N,a)\to(M,b)\) is a cofrontal if there is a germ of a smooth integrable subbundle \(K\subset TN\), \(K=(K_x)_{x\in(N,a)}\), of rank \(n-m\) such that \(K_x\) is in the kernel of the differential \(T_xN\to T_{f(x)}M\) of \(f\) for any \(x\in N\) near \(a\). A smooth map \(f:N\to M\) is a cofrontal if each germ is. For a foliation \(\mathcal{F}\) of codimension \(m\) on \(N\) any map \(N\to M\) that is constant on each leaf of \(\mathcal{F}\) is a cofrontal. When \(N\) is compact, any smooth map may be \(C^0\) approximated by a cofrontal. A classification is given of cofrontals with compact domain and one-dimensional fibres.