Mixed-model association analysis (MMAA) is the preferred tool for performing genome-wide association studies. However, existing MMAA tools often have long runtimes and high memory requirements. Here we present LDAK-KVIK, an MMAA tool for analysis of quantitative and binary phenotypes. LDAK-KVIK is computationally efficient, requiring less than 10 CPU hours and 5 Gb memory to analyze genome-wide data for 350,000 individuals. Using simulated phenotypes, we show that LDAK-KVIK produces well-calibrated test statistics for both homogeneous and heterogeneous datasets. When applied to real phenotypes, LDAK-KVIK has the highest power among all tools considered. For example, across 40 quantitative UK Biobank phenotypes (average sample size 349,000), LDAK-KVIK finds 16% more independent, genome-wide significant loci than classical linear regression, whereas BOLT-LMM and REGENIE find 15% and 11% more, respectively. LDAK-KVIK can also be used to perform gene-based tests; across the 40 quantitative UK Biobank phenotypes, LDAK-KVIK finds 18% more significant genes than the leading existing tool. Last, LDAK-KVIK produces state-of-the-art polygenic scores.