  Two divisors in $\mathbb P^n$ are said to be Cremona equivalent if there is a
Cremona modification sending one to the other. In this paper I study
irreducible cones in $\mathbb P^n$ and prove that two cones are Cremona
equivalent if their general hyperplane sections are birational. In particular I
produce examples of cones in $\mathbb P^3$ Cremona equivalent to a plane whose
plane section is not Cremona equivalent to a line in $\mathbb P^2$.
