The joke lands in the last two words, but the poem sets it up from the first line. A speaker announces, "I have a twin," and the claim is so casual that we almost accept it. The twin has a dog, and that dog "would follow me home." Then the poem turns on a pun. "Much correspondence there / has been between / our two lies." We expect "lives," and what we get is "lies," a single swapped letter that casts doubt on everything before it.
On the surface it is a small, odd anecdote about a stray loyalty. The dog belongs to the twin but chooses the speaker, as if it cannot tell the two apart, or can tell and prefers one. The verb tenses are worth noticing. The speaker "has" a twin, but the twin "had" a dog, so the animal is already lost to its owner. In a few syllables the poem sketches a small drama of divided belonging. Behind the deadpan tone, the twin starts to look like a double the speaker has invented or inherited, a second self who owns things that end up in the speaker's hands. The poem seems to be about the stories we tell about ourselves, and about how much invention goes into the "I" that says "I have."
The word "correspondence" carries most of that. It has two meanings, and the poem uses both. It means letters passing between two people, which suits twins writing to each other. It also means matching, one thing answering to another, the way two accounts or two halves of a pair correspond. The dog quietly joins both senses. It travels from one twin to the other like a messenger, and its movement is the only evidence we get that the twin exists at all. When the poem says the correspondence is between "our two lies," both senses curdle. The letters are fictions, and the matching is a matter of getting the stories to agree. Perhaps the twin is the speaker's fiction, or perhaps they are two people covering for each other.
The construction is plain. There is no end rhyme and no regular meter, only short lines that shrink as they go. The first two lines run to four syllables each, the third stretches to a relaxed eight ("but the dog would follow me home"), and then the poem tightens: six syllables, four, three. The shape suggests a story told easily that narrows toward a point. The third line is also the most natural-sounding, with its everyday phrase "follow me home," so the shift into "Much correspondence there / has been between" feels stiff by comparison. The inverted word order sounds like a letter or a legal document, and the mock-formality fits a poem about correspondence. The syntax is itself a bit of fakery, a dressed-up voice that suits a speaker who admits to lying.
Sound does the twinning too. "Twin" echoes inside "between," where you can almost hear it in the stressed syllable, and "two" repeats the same opening sound in the last line. The poem is built from pairs: speaker and twin, twin and dog, one lie and another. Its repeated *tw* sounds mimic what it describes. Even the title hides a double, since "correspondence" is both the letters and the likeness.
The imagery is minimal, and a dog on a road is the only picture we are given. That makes it work hard. A dog following someone home is a classic image of trust, which gives the "lies" at the end more bite, because honesty and loyalty are set against deception. The poem does not say whose lies they are, or whether they are harmful. "Our two lies" sounds almost companionable, like a shared secret or a joke between siblings.
What makes the poem worth reading is how much it asks of six lines and a one-letter slip. It shows that a pun can be more than decoration: here it overturns the meaning of what came before and leaves us unsure whether the twin, the dog, or the whole story is real. The last two words ask us to reread, and on a second reading "I have a twin" sounds less like a fact and more like the first lie. The poem makes its point by being what it describes, a short, plausible, slightly crooked piece of fiction passed from one person to another.