Several approaches have been proposed for numerically solving
lower dimensional differential algebraic equations (DAEs)
for which more classical methods such as backward differentiation
or implicit Runge-Kutta may not be appropriate. One of these
approaches is called explicit integration (EI). This approach
is based on solving nonlinear DAE derivative arrays using
nonlinear singular least squares methods. This results in a
computed ODE, called the least squares completion, whose solutions
contain those of the original DAE. This ODE is then integrated
by a classical numerical method. The additional dynamics of the
least squares completion can affect the numerical solution of 
the DAE. A recentpaper examined these additional dynamics and
developed an alternative least squares completion. In this paper
we study the problem of modifying both of these completions
in order to stabilize these extra dynamics.