  For a composition $I$ whose first part exceeds 1, we can define the multiple
$t$-value $t(I)$ as the sum of all the terms in the series for the multiple
zeta value $\zeta(I)$ whose denominators are odd. In this paper we show that if
$I$ is composition of $n\ge 3$, then $t(I)=(-1)^{n-1}t(\bar I)$ mod products,
where $\bar I$ is the reverse of $I$, and both sides are suitably regularized
when $I$ ends in 1. This result is not true for multiple zeta values, though
there is an argument-reversal result that does hold for them (and for multiple
$t$-values as well). We actually prove a more general version of this result,
and then use it to establish explicit formulas for several classes of multiple
$t$-values and interpolated multiple $t$-values.
