The European Solar Telescope (EST) is a 4.2-metre telescope that will be equipped with a multi-conjugate adaptive optics (MCAO) system to provide a high spatial resolution over a circular field of view with 60" diameter. The EST-MCAO testbed is a downscaled demonstrator of solar MCAO with similar requirements to those defined for EST. It has been designed and developed to identify and better understand the capabilities of this system. Before MCAO implementation, different AO configurations must be first evaluated in the testbed. Single conjugate adaptive optics for point-like sources has been identified as the first step towards MCAO for the EST. This configuration is based on the use of a deformable mirror with 820 actuators and a Shack-Hartmann wavefront sensor with 33x33 subapertures. The main objective of this paper is to present the results obtained in the EST-MCAO testbed when testing different phase reconstruction algorithms and closed-loop schemes to deal with SCAO for point-like sources. Center of gravity technique was proposed for local slope computation when using point-like sources. Both zonal and modal approaches, including SVD and their regularized least-squares versions, were evaluated and tested for the reconstruction. A closed-loop strategy based on a proportional-integral controller was initially proposed. The benefits of pseudo open-loop control were also evaluated. The performance of the algorithms was tested considering different seeing conditions. Finally, a comparison based on RMS wavefront error and Strehl Ratio was conducted.