The electrification of the power train in the automotive industry leads to the requirement of electrical connectors with high ampacities. These connectors are often realized using ultrasonic bonding technology. Substitution of ultrasonic welding by laser welding allows an increase of ribbon cross section by a factor of 5 and thus a similar increase of the maximum transferred current. The increased cross section leads to higher loads (at least by a factor of 5) applied to the weld seam during the process. To minimize the heat input, the weld seam strength in shear direction shall be maximized. The influence of different laser parameters on the ultimate tensile shear stress in lap joint configuration is investigated, based on representative specimen geometries (10 × 0.3 mm2). The variable parameters are: laser wavelength (IR around 1050 nm + frequency doubled 515 nm), focal diameters (42–300 μm), different temper conditions of the base material, process parameters (laser power 0.6–4 kW and feed rate 50–800 mm/s), and welding strategies (single pass welding, spatial beam modulation). The material used is Cu-ETP (>99.9% Cu). For all the investigated parameters, the observed failure mode is “fracture in the fusion zone.” The ultimate tensile shear stress for all experiments is around 188 N/mm2 even for parameter changes in the order of one magnitude. This is in contrast to the assumed relation between laser parameters and the mechanical properties. This contrast will be discussed.