I like the way he abandoned strict rhyme and regular metre after his first three collections, and worked at a freer verse from his Pulitzer winning fourth collection 'At the End of the Open Road' (1963) until his last 'There You Are' (1995).
I like very much his commitment to plain speech that was evident from the start of his career and found even more varied expression once the shift mentioned above had taken place.
Before that change, whilst their was already the commitment to unshowy diction, the poems read like an outsider trying to write their way into a tradition - a formal, romantic tradition that derives from another continent in a previous century and which I think must have already started to sound archaic to most mid-twentieth century American ears.
His early war poems, for example, are embarrassingly poetic, not least because he is more often interested in the experience of being a young poet, doing the American in Paris routine, than with the horror and hardship of war. They certainly can't compare with the war poetry of say Randall Jarrell or Keith Douglas.
However, this outsider status also eventually served Simpson well in providing him with a range of subject matter for his poems. His poems return to his early life in Jamaica and Russian Jewish ancestry on his mother's side, whilst exploring his ever-deepening sense of the American way of life - he moved to the States when he was seventeen.
I can hear Chekhov and Hemingway behind the poetry of the second half of his career. Indeed, prose writers rather than poets come to mind when thinking about the influences on his work.
Of those influenced in turn by Simpson, I can hear Carver (unsurprising), Simic and Kleinzhaler (there are many good city poems with a cast of urban eccentrics) and on this side of the Atlantic, Hugo Williams (Simpson was at the height of his poetic career and published in the UK by OUP when Hamilton and Williams et al were honing their brand of plain spoken minimalism).
I like the narrative element in most of his poetry. As he states in the Preface to his Collected Poems, he 'can hardly enjoy a poem that is all idea and has no visible place or action.' This means the poems are frequently about the lives of other people, other places, and how the poet relates to them.
I love the careful use of punctuation in most of his poems. I like the way his poems fill the page. They are not often long but when they are they are made up of irregular length stanzas and broken into clear sections, each one functioning like a paragraph. He is a poet with the skill of a very accomplished prose writer.
Description is noun-based, deft and vivid, giving rise to a tremendous amount of suggestion, discomfort and ominous silence. Chekhov and Hemingway again come to mind.
Reading his Collected Poems, one also becomes aware of an interest in Buddhist thought and meditation. There is clear-eyed observation but also humility and compassion, especially in the poems about broken lives.
Later on the poems shift from the city to suburbia. Updike comes to mind thinking about the poems describing marriage and small-town family life. In such poems about the lives of ordinary individuals the novelist's imagination is very much evident.
In fact, one can't help but think of Wordsworth's undertaking in the Lyrical Ballads, updated to near-contemporary America. And the aspect of American life Simpson most frequently portrays is the failure of intimate relationships, a loosening of the social glue.