  Let $f$ be a continuous circle map and let $F$ be a lifting of $f$. In this
note we study how the existence of a large orbit for $F$ affects its set of
periods. More precisely, we show that, if $F$ is of degree $d\geq 1$ and has a
periodic orbit of diameter larger than 1, then $F$ has periodic points of
period $n$ for all integers $n\geq 1$, and thus so has $f$. We also give
examples showing that this result does not hold when the degree is non
positive.
