  The \theta-closed hull of a set A in a topological space is the smallest set
C containing A such that, whenever all $closed$ neighborhoods of a point
intersect C, this point is in C.
  We define a new topological cardinal invariant function, the
$\theta-bitighness small number$ of a space X, bts_theta(X), and prove that in
every topological space X, the cardinality of the theta-closed hull of each set
A is at most |A|^{bts_theta(X)}. Using this result, we synthesize all earlier
results on bounds on the cardinality of theta-closed hulls.
  We provide applications to P-spaces and to the almost-Lindelof number.
