  Extending a result of R. de la Vega, we prove that an infinite homogeneous
compactum has cardinality $\mathfrak{c}$ if either it is the union of countably
many dense or finitely many arbitrary countably tight subspaces. The question
if every infinite homogeneous and $\sigma$-countably tight compactum has
cardinality $\mathfrak{c}$ remains open.
  We also show that if an arbitrary product is $\sigma$-countably tight then
all but finitely many of its factors must be countably tight.
