  A sequence of recent studies show that even in the simple setting of a single
seller and a single buyer with additive, independent valuations over $m$ items,
the revenue-maximizing mechanism is prohibitively complex. This problem has
been addressed using two main approaches: (i) Approximation: the best of two
simple mechanisms (sell each item separately, or sell all the items as one
bundle) gives $1/6$ of the optimal revenue [BILW14]. (ii) Enhanced competition:
running the simple VCG mechanism with additional $m$ buyers extracts at least
the optimal revenue in the original market [EFFTW17]. Both approaches, however,
suffer from severe drawbacks: On the one hand, losing $83\%$ of the revenue is
hardly acceptable in any application. On the other hand, attracting a linear
number of new buyers may be prohibitive. Our main result is that by combining
the two approaches one can achieve the best of both worlds. Specifically, for
any constant $\epsilon$ one can obtain a $(1-\epsilon)$ fraction of the optimal
revenue by running simple mechanisms --- either selling each item separately or
selling all items as a single bundle --- with substantially fewer additional
buyers: logarithmic, constant, or even none in some cases.
