  The problem of existence of stable nonlinear groups of gravity waves in deep
water is revised by means of laboratory and numerical simulations with the
focus on intense waves. Wave groups with steepness up to $A_{cr} \omega_m^2 /g
\approx 0.30$ are reproduced in laboratory experiments ($A_{cr}$ is the wave
crest amplitude, $\omega_m$ is the mean angular frequency and $g$ is the
gravity acceleration). We show that the groups remain stable and exhibit
neither noticeable radiation nor structural transformation for more than 60
wave lengths or about 15-30 group lengths. These solitary wave patterns differ
from the conventional envelope solitons, as only a few individual waves are
contained in the group. Very good agreement is obtained between the laboratory
results and strongly nonlinear numerical simulations of the potential Euler
equations. The envelope soliton solution of the nonlinear Schr\"odinger
equation is shown to be a reasonable first approximation for specifying the
wavemaker driving signal. The short intense envelope solitons possess vertical
asymmetry similar to regular Stokes waves with the same frequency and crest
amplitude. Nonlinearity is found to have remarkably stronger effect on the
speed of envelope solitons in comparison to the nonlinear correction to the
Stokes wave velocity.
