Context :

Aims : One of the major uncertainties in close binary evolution is the efficiency of mass transfer \beta : the fraction of transferred mass that is accreted by a secondary star .
We attempt to constrain the mass-transfer efficiency for short-period massive binaries undergoing case A mass transfer .

Methods : We present a grid of about 20,000 detailed binary evolution tracks with primary masses 3.5–35 \mathrm { M } _ { \odot } , orbital periods 1–5 days at a metallicity Z = 0.004 , assuming both conservative and non-conservative mass transfer .
We perform a systematic comparison , using least-squares fitting , of the computed models with a sample of 50 double-lined eclipsing binaries in the Small Magellanic Cloud , for which fundamental stellar parameters have been determined .
About 60 \% of the systems are currently undergoing slow mass transfer .

Results : In general we find good agreement between our models and the observed detached systems .
However , for many of the semi-detached systems the observed temperature ratio is more extreme than our models predict .
For the 17 semi-detached systems that we are able to match , we find a large spread in the best fitting mass-transfer efficiency ; no single value of \beta can explain all systems .
We find a hint that initially wider systems tend to fit better to less conservative models .
We show the need for more accurate temperature determinations and we find that determinations of surface abundances of nitrogen and carbon can potentially constrain the mass-transfer efficiency further .

Conclusions :