\begin{abstract}
By solving numerically the full set of hydrodynamic equations governing the
pulsation of a bubble,  we show that shock waves are often absent in a stable
sonoluminescing bubble. Nevertheless, for a wide range of physical parameters,
a smooth compressional wave emerges and heats up the bubble, and the resulting
black-body radiations have pulse heights and widths that agree with 
experimental data.  Shock waves, being much less robust, are not essential
for stable single-bubble sonoluminescence.
\end{abstract}
\pacs{PACS numbers: 78.60.Mq, 47.40.-x, 44.10.+i, 43.25.+y}