We study two classes of view update problems in relational databases. We are given a source database S, a monotone query Q, and the view Q(S) generated by the query. The first problem that we consider is the classical view deletion problem where we wish to identify a minimal set T of tuples in S whose deletion will eliminate a given tuple t from the view. We study the complexity of optimizing two natural objectives in this setting, namely, find T to minimize the side-effects on the view, and the source, respectively. For both objective functions, we show a dichotomy in the complexity. Interestingly, the problem is either in P or is NP-hard, for queries in the same class in either objective function. The second problem in our study is the annotation placement problem. Suppose we annotate an attribute of a tuple in S. The rules for carrying the annotation forward through a query are easily stated. On the other hand, suppose we annotate an attribute of a tuple in the view Q(S), what anno...