  Extending Sparks's theorem, we determine the cardinality of the lattice of
$(C_1,C_2)$-clonoids of Boolean functions in the cases where the target clone
$C_2$ is the clone of projections. Moreover, we explicitly describe the
$(C_1,C_2)$-clonoids of Boolean functions in the cases where the source clone
$C_1$ is one of the four clones of monotone functions or contains the
discriminator function.
