A partial (n, k, t)λ-system is a pair(X, B) where X is an n-set of vertices and B is a collection of k-subsets of X called blocks such that each t-set of vertices is a subset of at most λ blocks. A sequencing of such a system is a labelling of its vertices with distinct elements of {0,..., n − 1}. A sequencing is -block avoiding or, more briefly, -good if no block is contained in a set of vertices with consecutive labels. Here we give a short proof that, for fixed k, t and λ, any partial (n, k, t)λ-system has an -good sequencing for some = �(n1/t ) as n becomes large. This improves on results of Blackburn and Etzion, and of Stinson and Veitch. Our result is perhaps of most interest in the case k = t +1 where results of Kostochka, Mubayi and Verstraëte show that the value of cannot be increased beyond �((n log n)1/t ). A special case of our result shows that every partial Steiner triple system (partial (n, 3, 2)1- system) has an -good sequencing for each positive integer 0.0908 n1/2.