Context : On the order of 20 % of the very metal-poor stars in the Galaxy exhibit large carbon enhancements .
It is important to establish which astrophysical sites and processes are responsible for the elemental abundance patterns of this early Galactic population .

Aims : We seek to understand the nature of the progenitors of three main-sequence turnoff Carbon-Enhanced Metal-Poor ( CEMP ) stars , CSÂ 31080 - 095 , CSÂ 22958 - 042 , and CSÂ 29528 - 041 , based on a detailed abundance analysis .

Methods : From high-resolution VLT/UVES spectra ( R \sim 43 , 000 ) , we determine abundances or upper limits for Li , C , N , O , and other important elements , as well as ^ { 12 } C/ ^ { 13 } C isotopic ratios .

Results : All three stars have -3.30 \leq [ Fe / H ] \leq - 2.85 and moderate to high CNO abundances .
CSÂ 22958 - 042Â is one of the most carbon-rich CEMP stars known ( [ C/Fe ] = +3.2 ) , while CSÂ 29528 - 041Â ( one of the few N-enhanced metal-poor stars known ) is one of the most nitrogen rich ( [ N/Fe ] = +3.0 ) .
Oxygen is very high in CSÂ 31080 - 095Â ( [ O/Fe ] = +2.35 ) and in CSÂ 22958 - 042Â ( [ O/Fe ] = +1.35 ) .
All three stars exhibit [ Sr/Fe ] < 0 ; Ba is not detected in CSÂ 22958 - 042Â ( [ Ba/Fe ] < -0.53 ) , but it is moderately enhanced ( [ Ba/Fe ] \sim 1 ) in the other two stars .
CSÂ 22958 - 042Â displays one of the largest sodium overabundances yet found in CEMP stars ( [ Na/Fe ] = +2.8 ) .
CSÂ 22958 - 042Â has ^ { 12 } C/ ^ { 13 } C = 9 , similar to most other CEMP stars without enhanced neutron-capture elements , while ^ { 12 } C/ ^ { 13 } C \geq 40 in CSÂ 31080 - 095 .
CSÂ 31080 - 095Â and CSÂ 29528 - 041Â have A ( Li ) \sim 1.7 , below the Spite Plateau , while Li is not detected in CSÂ 22958 - 042 .

Conclusions : CSÂ 22958 - 042Â is a CEMP-no star , but the other two stars are in no known class of CEMP star and thus either constitute a new class or are a link between the CEMP-no and CEMP-s classes , adding complexity to the abundance patterns for CEMP stars .
We interpret the abundance patterns in our stars to imply that current models for the presumed AGB binary progenitors lack an extra-mixing process , similar to those apparently operating in RGB stars .