  We propose a new, very efficient algorithm for sampling of random surfaces in
the Monte Carlo simulations, based on so-called baby universe surgery, i.e.
cutting and pasting of baby universes. It drastically reduces slowing down as
compared to the standard local flip algorithm, thereby allowing simulations of
large random surfaces coupled to matter fields. As an example we investigate
the efficiency of the algorithm for 2d simplicial gravity interacting with a
one-component free scalar field. The radius of gyration is the slowest mode in
the standard local flip/shift algorithm. The use of baby universe surgery
decreases the autocorrelation time by three order of magnitude for a random
surface of $0.5 \cdot 10^5$ triangles, where it is found to be $\tau_{int} =
150 \pm 31$ sweeps.
