  Given two $n$-element structures, $\mathcal{A}$ and $\mathcal{B}$, which can
be distinguished by a sentence of $k$-variable first-order logic
($\mathcal{L}^k$), what is the minimum $f(n)$ such that there is guaranteed to
be a sentence $\phi \in \mathcal{L}^k$ with at most $f(n)$ quantifiers, such
that $\mathcal{A} \models \phi$ but $\mathcal{B} \not \models \phi$? We present
various results related to this question obtained by using the recently
introduced QVT games. In particular, we show that when we limit the number of
variables, there can be an exponential gap between the quantifier depth and the
quantifier number needed to separate two structures. Through the lens of this
question, we will highlight some difficulties that arise in analysing the QVT
game and some techniques which can help to overcome them. As a consequence, we
show that $\mathcal{L}^{k+1}$ is exponentially more succinct than
$\mathcal{L}^{k}$. We also show, in the setting of the existential-positive
fragment, how to lift quantifier depth lower bounds to quantifier number lower
bounds. This leads to almost tight bounds.
