Context : Aims : To investigate the stellar and wind properties of a sample of late-type O dwarfs in order to address the weak wind problem . Methods : Far-UV to optical spectra of five Galactic O stars were analyzed : HD 216898 ( O9IV/O8.5V ) , HD 326329 ( O9V ) , HD 66788 ( O8V/O9V ) , \zeta Oph ( O9.5Vnn ) , and HD 216532 ( O8.5V ( ( n ) ) ) . We used a grid of TLUSTY models to obtain effective temperatures , gravities , rotational velocities , and to identify wind lines . The wind parameters of each object were obtained by using expanding atmosphere models from the CMFGEN code . Results : We found that the spectra of our sample have mainly a photospheric origin . A weak wind signature is seen in C iv \lambda \lambda 1548,1551 , from where mass-loss rates consistent with previous CMFGEN results regarding O8-O9V stars were obtained ( \sim 10 ^ { -10 } -10 ^ { -9 } M _ { \odot } yr ^ { -1 } ) . A discrepancy of roughly 2 orders of magnitude is found between these mass-loss rates and the values predicted by theory ( \dot { M } _ { Vink } ) , confirming a breakdown or a steepening of the modified wind momentum-luminosity relation at log L _ { \star } / L _ { \odot } \lesssim 5.2 . We have estimated the carbon abundance for the stars of our sample and concluded that its uncertainty can not cause the weak wind problem . Upper limits on \dot { M } were established for all objects using lines of different ions , namely , P v \lambda \lambda 1118,1128 , C iii \lambda 1176 , N v \lambda 1239,1243 , Si iv \lambda \lambda 1394,1403 , and N iv \lambda 1718 . All the values obtained are also in disagreement with theoretical predictions , bringing support to the reality of weak winds . Together with C iv \lambda \lambda 1548,1551 , the use of N v \lambda 1239,1243 results in the lowest mass-loss rates : the upper limits indicate that \dot { M } must be less than about -1.0 dex \dot { M } _ { Vink } . Regarding the other transitions , the upper limits obtained still point to low rates : \dot { M } must be less than about ( -0.5 \pm 0.2 ) dex \dot { M } _ { Vink } . We studied the behavior of the H \alpha line with different mass-loss rates . For two stars , only models with very low \dot { M } ’ s provide the best fit to the UV and optical spectra . We explored ways to fit the observed spectra with the predicted mass-loss rates ( \dot { M } _ { Vink } ) . By using large amounts of X-rays , we verified that few wind emissions takes place , as in weak winds . However , unrealistic X-rays luminosities had to be used ( log L _ { X } / L _ { Bol } \gtrsim - 3.5 ) . The validity of the models used in our analyses is discussed . Conclusions :