Breeding schemes that utilize modern breeding methods like genomic selection (GS) and speed breeding (SB) have the potential to accelerate genetic gain for different crops. We investigated through stochastic computer simulation the advantages and disadvantages of adopting both GS and SB (SpeedGS) into commercial breeding programs for allogamous crops. In addition, we studied the effect of omitting one or two selection stages from the conventional phenotypic scheme on GS accuracy, genetic gain, and inbreeding. As an example, we simulated GS and SB for five traits (heading date, forage yield, seed yield, persistency, and quality) with different genetic architectures and heritabilities (0.7, 0.3, 0.4, 0.1, and 0.3; respectively) for a tall fescue breeding program. We developed a new method to simulate correlated traits with complex architectures of which effects can be sampled from multiple distributions, e.g. to simulate the presence of both minor and major genes. The phenotypic selection scheme required 11 years, while the proposed SpeedGS schemes required four to nine years per cycle. Generally, SpeedGS schemes resulted in higher genetic gain per year for all traits especially for traits with low heritability such as persistency. Our results showed that running more SB rounds resulted in higher genetic gain per cycle when compared to phenotypic or GS only schemes and this increase was more pronounced per year when cycle time was shortened by omitting cycle stages. While GS accuracy declined with additional SB rounds, the decline was less in round three than in round two, and it stabilized after the fourth SB round. However, more SB rounds resulted in higher inbreeding rate, which could limit long-term genetic gain. The inbreeding rate was reduced by approximately 30% when generating the initial population for each cycle through random crosses instead of generating half-sib families. Our study demonstrated a large potential for additional genetic gain from combining GS and SB. Nevertheless, methods to mitigate inbreeding should be considered for optimal utilization of these highly accelerated breeding programs.