  The paper is related to the following question of P.~L.~Ul'yanov: is it true
that for any $2\pi$-periodic continuous function $f$ there is a uniformly
convergent rearrangement of its trigonometric Fourier series? In particular, we
give an affirmative answer if the absolute values of Fourier coefficients of
$f$ decrease. Also, we study a problem how to choose $m$ terms of a
trigonometric polynomial of degree $n$ to make the uniform norm of their sum as
small as possible.
