  Allowing for antineutrinos ($\bar\nu_x$) and sterile neutrinos ($\nu_s$) to
accompany LMA oscillations, we derive in a model independent way, upper bounds
on their components in the solar flux, using the recent data from SNO and
SuperKamiokande. Along with the general case (LMA + $\bar\nu_x$ + $\nu_s$) we
consider the special cases where only $\bar\nu_x$ or $\nu_s$ are present. We
obtain an upper bound on $\bar\nu_x$ which is independent of the $\nu_s$
component. In the no sterile case we obtain upper and lower bounds on $f_B$,
the SSM normalization factor. We also investigate in the general case the
common parameter range for $f_B$ and the $\bar\nu_x$, $\nu_s$ components and
find that the upper bound on $\nu_s$ is hardly sensitive to the $\bar\nu_x$
component. In the absence of $\bar\nu_x$ we recover the $\nu_s$ upper bound
existing in the literature. We finally present a simple $\chi^2$ analysis of
all four cases considered.
