Context :

Aims : We present the first Doppler imaging study of the two rapidly rotating , single K-giants DP CVn and DI Psc in order to study the surface spot configuration and to pinpoint their stellar evolutionary status .

Methods : Optical spectroscopy and photometry are used to determine the fundamental astrophysical properties .
Doppler imaging is applied to recover the surface temperature distribution for both stars , while photometric light-curve inversions are carried out for studying the long-term changes of the surface activity of DP CVn .
Surface differential rotation of DP CVn is estimated from cross-correlating the available subsequent Doppler reconstructions separated by roughly one rotation period .

Results : Both stars appear to have higher than normal lithium abundance , LTE \log n of 2.28 ( DP CVn ) and 2.20 ( DI Psc ) , and are supposed to be located at the end of the first Li dredge-up on the RGB .
Photometric observations reveal rotational modulation with a period of 14.010 d ( DP CVn ) and 18.066 d ( DI Psc ) .
Doppler reconstructions from the available mapping lines well agree in the revealed spot patterns , recovering rather low latitude spots for both stars with temperature contrasts of \Delta T \approx 600 - 800 K below the unspotted photospheric background .
Spots at higher latitudes are also found but either with less contrast ( DP CVn ) or with smaller extent ( DI Psc ) .
A preliminary antisolar-type differential rotation with \alpha = -0.035 is found for DP CVn from cross-correlating the subsequent Doppler images .
Long-term photometric analysis supports the existence of active longitudes , as well as the differential rotation .

Conclusions :