The paper presents a general method of imposing constraints in formal concept analysis of tabular data describing objects and their attributes. The constraints represent a user-defined requirements which are supplied along with the input data table. The main effect is to filter-out outputs of the analysis (conceptual clusters and if-then rules) which are not compatible with the constraint, in a computationally efficient way (polynomial time delay algorithm without the need to compute all outputs). Our approach covers several examples studied before, e.g. extraction of closed frequent itemsets in generation of non-redundant association rules. We present motivations, foundations, and examples.