In structural optimization, the level set method is known as a well-established approach for shape and topology optimization. However, special care must be taken, if the design domains are sparsely-filled and slender. Using steepest descent-type level set methods, slender structure topology optimizations tend to instabilities and loss of structural cohesion. A sole step size control or a selection of more complex initial designs only help occasionally to overcome these issues and do not describe a universal solution. In this paper, instead of updating the level set function by solving a Hamilton–Jacobi partial differential equation, an adapted algorithm for the update of the level set function is utilized, which allows an efficient and stable topology optimization of slender structures. Including different adaptations, this algorithm replaces unacceptable designs by modifying both the pseudo-time step size and the Lagrange multiplier. Besides, adjustments are incorporated in the normal velocity formulation to avoid instabilities and achieve a smoother optimization convergence. Furthermore, adding filtering-like adaptation terms to the update scheme, even in case of very slender structures, the algorithm is able to perform topology optimization with an appropriate convergence speed. This procedure is applied for compliance minimization problems of slender structures. The stability of the optimization process is shown by 2D numerical examples. The solid isotropic material with penalization (SIMP) method is used as an alternative approach to validate the result quality of the presented method. Finally, the simple extension to 3D optimization problems is addressed, and a 3D optimization example is briefly discussed.