  We critically examine the possibility of determining the parity of the
$\Theta^+(1540)$ from the reactions $NN\to \Theta^+Y$ ($Y$ = $\Lambda$,
$\Sigma$) recently discussed in the literature. Specifically, we study the
energy dependence of those observables that were suggested to be the most
promising ones to unravel the parity of the $\Theta^+$, namely the spin
correlation coefficient $A_{xx}$, and the spin transfer coefficient $D_{xx}$.
We show that the energy dependence of $\sigma_0(1+A_{xx})$, corresponding to
the spin-triplet production cross section, guarantees unambiguous information
on the parity of the $\Theta^+$. Here, $\sigma_0$ denotes the unpolarized cross
section. Also, the possibility to determine the parity of the $\Theta^+$
through the energy dependence of $\sigma_0D_{xx}$ is discussed.
