Method for producing a single-crystal component comprising a nickel-based superalloy, or a directionally solidified component, wherein the component is first cast in a known manner in a mould forming a structure having a dendrite, and then a solution-annealing process is carried out for homogenization of the cast structure of the component and a two-stage precipitation heat treatment is performed, characterised by the following steps: A) determining the dendrite arm spacing (λ) in different areas of the cast component, B) identifying the slowest diffusion element in the composition of the respective nickel-based superalloy for determining the diffusion coefficient, C) calculating the required time (t) necessary to reduce the segregation of this slowest diffusion element to ≤ 5% at a solution annealing temperature (T 1) which is firstly lower than the starting melt temperature (T mi) and secondly however high enough to lie within the necessary heat treatment window, D) solution-annealing the cast component, comprising heating of the component to the solution-annealing temperature (T 1), holding at this temperature (T 1) for the time (t) calculated in step C), and quenching from the temperature (T 1) to room temperature with a speed ≥ 50°C/min, E) carrying out the two-stage precipitation treatment for separating the γ' phase at respectively lower temperatures (T 2) and (T 3) following step D), wherein the first stage of the precipitation treatment comprises carrying out an HIP process with an isostatic pressure (p) greater than 160 MPa at the holding temperature (T 2) and subsequent cooling from the temperature (T 2) to room temperature with a cooling rate ≥ 50°C/min, and the subsequent second stage of the precipitation treatment comprises heat treatment of the component at a holding temperature (T 3) and a subsequent cooling from the temperature (T 3) to room temperature with a cooling rate of 10-50°C/min. A) determining the dendrite arm spacing (λ) in different areas of the cast component, B) identifying the slowest diffusion element in the composition of the respective nickel-based superalloy for determining the diffusion coefficient, C) calculating the required time (t) necessary to reduce the segregation of this slowest diffusion element to ≤ 5% at a solution annealing temperature (T 1) which is firstly lower than the starting melt temperature (T mi) and secondly however high enough to lie within the necessary heat treatment window, D) solution-annealing the cast component, comprising heating of the component to the solution-annealing temperature (T 1), holding at this temperature (T 1) for the time (t) calculated in step C), and quenching from the temperature (T 1) to room temperature with a speed ≥ 50°C/min, E) carrying out the two-stage precipitation treatment for separating the γ' phase at respectively lower temperatures (T 2) and (T 3) following step D), wherein the first stage of the precipitation treatment comprises carrying out an HIP process with an isostatic pressure (p) greater than 160 MPa at the holding temperature (T 2) and subsequent cooling from the temperature (T 2) to room temperature with a cooling rate ≥ 50°C/min, and the subsequent second stage of the precipitation treatment comprises heat treatment of the component at a holding temperature (T 3) and a subsequent cooling from the temperature (T 3) to room temperature with a cooling rate of 10-50°C/min.