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We study compositions (ordered partitions) of  n . More particularly, our focus is on the bargraph representation of compositions which include or avoid squares of size  s  ×  s . We also extend the definition of a Durfee square (studied in integer partitions) to be the largest square which lies on the base of the bargraph representation of a composition (i.e., is ‘grounded’). Via generating functions and asymptotic analysis, we consider compositions of  n  whose Durfee squares are of size less than  s  ×  s . This is followed by a section on the total and average number of grounded  s  ×  s  squares. We then count the number of Durfee squares in compositions of  n .