Advances in whole-genome genotyping and sequencing have allowed genome-wide analyses of association, prediction and heritability in many organisms. However, the application of such analyses to bacteria is still in its infancy, being limited by difficulties including the plasticity of bacterial genomes and their strong population structure. Here we propose a suite of genome-wide analyses for bacteria that combines methods from human genetics and previous bacterial studies, including linear mixed models, elastic net and LD-score regression. We introduce innovations such as frequency-based allele coding, testing for both insertion/deletion and nucleotide effects and partitioning heritability by genome region. Using a previously-published large cohort study, we analyse three phenotypes of a major human pathogen Streptococcus pneumoniae , including the first analyses of minimum inhibitory concentrations (MIC) for each of two antibiotics, penicillin and ceftriaxone. We show that these are very highly heritable leading to high prediction accuracy, which is explained by many genetic associations identified under good control of population structure effects. In the case of ceftriaxone MIC, these results are surprising because none of the isolates was resistant according to the inhibition zone diameter threshold. We estimate that just over half of the heritability of penicillin MIC is explained by a known drug-resistance region, which also contributes around a quarter of the heritability of ceftriaxone MIC. For the within-host survival phenotype carriage duration, no reliable associations were found but we observed moderate heritability and prediction accuracy, indicating a polygenic trait. While generating important new results for S. pneumoniae , we have critically assessed existing methods and introduced innovations that will be useful for future large-scale population genomics studies to help decipher the genetic architecture of bacterial traits. Author summary Genome-wide association, prediction and heritability analyses in bacteria are beginning to help unravel the genetic underpinnings of traits such as antimicrobial resistance, virulence, within-host survival and transmissibility. Progress to date is limited by challenges including the effects of strong population structure and variable recombination, and the many gaps in sequence alignments including the absence of entire genes in many isolates. More work is required to critically asses and develop methods for bacterial genomics. We address this task here, using a range of existing methods from bacterial and human genetics, such as linear mixed models, elastic net and LD-score regression. We adapt these methods to introduce new analyses, including separate assessment of gap and nucleotide effects, a new allele coding for association analyses and a method to partition heritability into genome regions. We analyse within-host survival and two antimicrobial response traits of Streptococcus pneumoniae , identifying many novel associations while demonstrating good control of population structure and accurate prediction. We present both new results for an important pathogen and methodological advances that will be useful in guiding future studies in bacterial population genomics.