  Refining some results of S. S. Dragomir, several new reverses of the
generalized triangle inequality in inner product spaces are given. Among
several results, we establish some reverses for the Schwarz inequality. In
particular, it is proved that if $a$ is a unit vector in a real or complex
inner product space $(H;< .,.>)$, $r, s>0, p\in(0,s], D=\{x\in H,\|rx-sa\|\leq
p\}, x_1, x_2\in D-\{0\}$ and $
\alpha_{r,s}=\min\{\frac{r^2\|x_k\|^2-p^2+s^2}{2rs\|x_k\|}: 1\leq k\leq 2 \}$,
then $$\frac{\|x_1\|\|x_2\|-Re< x_1,x_2>}{(\|x_1\|+\|x_2\|)^2}\leq
\alpha_{r,s}.$$
