Over the years, one has often been tempted to ask, "Will the real Louis Simpson please stand up?" For there have been several. There was the correct but amazingly precocious young Briton from Jamaica, the coeditor of "New Poets of England and America," a few of whose poems are preserved in the opening sections of "People Live Here." There was the brief but shrill convert to the school of Robert Bly. There was the author of critical books like "A Revolution in Taste," which seems to me all too English in its breezy mixture of gossip and snap judgments. Finally, there is the wonderful poet of the last 10 years, whose bare, unadorned poems of the common life remind me of Randall Jarrell.

That Mr. Simpson knows where his best work is to be found is indicated by both the title of "People Live Here," a selection of poems...