Moniza Alvi's Europa (Bloodaxe £7.95) is published simultaneously with Split World: Poems 1990-2005 (Bloodaxe £10.95), a substantial selection from five earlier volumes. The new book renews and extends ambitiously her fascination with one characteristic subject of the previous work, the “split” between the East of her ancestry (she was born in Pakistan and grew up in England) and the history and myths of the West.

Its centrepiece, Europa and the Bull, addresses the legend of the abduction and rape of King Agenor's daughter by Jupiter in the shape of the bull, with its “tender glance” and “wordless sympathy”. Her treatment of the tale seems oddly gentle at first; but her sequence of 25 short sections is complemented by further, harsher variations on the Europa myth and on the broader “dark theme” of trauma and its aftermath in history and in individuals. Alvi's is a quiet voice that owes something to the French poet Jules Supervielle (1884-1960), who manages to be both reticent and eerily disturbing; she continues here to translate Supervielle with skill and sensitivity. But what she has to say about outsider art, honour killing or the Iraq war (in Hanging) is memorable and entirely her own in style.

Admirers of Selima Hill's poetry will come to The Hat (Bloodaxe £7.95) expecting brief, painful, inconsequentially hilarious poems. They will not be disappointed, but they should look also at her own, large selected edition, Gloria (Bloodaxe £12), which shows her to advantage in a more relaxed, expansive vein. There is a simple problem with the 50-odd poems in the smaller volume, only two of which exceed 10 lines: they either clinch their metaphors for pain and isolation and force themselves into one's memory; or they rely on a kind of unresolved riddling to convey “a woman's struggle to regain her identity”.

King of Trout has just two lines: “His body, like a partly jewelled trout,/doesn't make a sound. Thank God for that!” Fortunately, Hill's menagerie of distress, with its tortoise, piglets, geese, horses (in particular), ducks and porcupines, performs more effectively when the ideas are simultaneously disarming, precise and apt: “Women are like gardens where gold snails/are walking back and forth in the rain/and as they walk their curious long feet/are feeling for a surface to console them.” And the poems that do succeed outnumber the bewildering failures.

Wendy Cope's Two Cures for Love: Selected Poems 1979-2006 (Faber £12.99) arrives with the addition by the poet of dates for the composition of poems (always necessary?) and meticulous notes in case of any continuing confusion among students about her literary references (so will this book, also, feature on syllabuses?). There are some new poems, but mainly this is an opportunity to read the best of her work in one volume.

It reads as freshly as it did when she first found form 20 years ago as the most accomplished and discerning of parodists. Her justly celebrated (and extremely genial) jokes at the expense of TS Eliot, John Berryman and Geoffrey Hill among others are testimony to her command of form - seen also in sonnets, triplets, villanelles and ballades. But Cope also has a special second gift, for investing the most ordinary (but important) of emotions - sentimental memories of parents, unrequited love for impossible men - with comic dignity. Apart from anything else, she is a successful non-permissive love poet in a permissive age.

In complete contrast is Jorie Graham's Sea Change (Carcanet, £9.95). In some ways very remarkable work, this volume deserves attention as a style in American poetry to which English poets will, at some time, have to pay respect. Sea Change contains 19 bulky two-to-three page poems, done in long single lines alternating with up to five short, staccato lines. Graham can be a poet of brilliant, boisterous energy - try reading aloud the title poem or Later in Life, or Nearing Dawn. But she sometimes seems trapped in this form, and unwillingly pulled along by it. The need to keep it going can produce turgidly rhetorical patches and dilemmas about how to end. These are poems that travel with energetic hope but don't always arrive.

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