  Assuming the existence of a strong cardinal and a measurable cardinal above
it, we construct a model of $ZFC$ in which for every singular cardinal
$\delta$, $\delta$ is strong limit, $2^\delta=\delta^{+3}$ and the tree
property at $\delta^{++}$ holds. This answers a question of Friedman, Honzik
and Stejskalova [8]. We also produce, relative to the existence of a strong
cardinal and two measurable cardinals above it, a model of $ZFC$ in which the
tree property holds at all regular even cardinals. The result answers questions
of Friedman-Halilovic [5] and Friedman-Honzik [6].
