Karst conduit shapes have a high influence on fluid flows. As these underground hidden systems are partially inaccessible, their stochastic simulation is an essential tool to assess the uncertainties related to these highly exploited water resources. The object-distance simulation method (ODSIM) is a hybrid dual-scale approach that has been recently proposed to model geological underground structures due to late processes such as dolomitized rocks, mineralized veins or karsts. Using a perturbed Euclidean distance field around a curve representing roughly the conduit centre and called a skeleton, the resulting shapes are globally cylindrical-like 3D envelopes. But at a drain scale, karstic conduits are elongated along weakness planes such as lithostratigraphic horizons, bedding planes, fractures or faults. In addition to those planes the influence of the water table is added. This work presents different improvements of ODSIM methodology for simulating more realistic shapes in the particular case of karst Firstly, we propose using a custom distance field computed with a fast marching method. Considering the ``velocity'' field to be proportional to the permeability allows the resulting features to be elongated along the weakness planes. Secondly, to handle specific shapes due to the proximity of the water table, such as trenches or notches, we impose areas of higher velocity between the skeleton and the water table. Finally, we generate a custom random threshold with several variograms and/or distributions depending on the different features integrated in the ``velocity'' field. Applied on different models, it is shown that the resulting karst conduits have more realistic shapes than those obtained with the previous workflow, while the variability of structures which can be modelled with ODSIM is preserved.