Production of massive DNA sequence data sets is transforming phylogenetic inference, but best practices for analyzing such data sets are not well established. One uncertainty is robustness to missing data, particularly in coalescent frameworks. To understand the effects of increasing matrix size and loci at the cost of increasing missing data, we produced a 90 taxon, 2.2 megabase, 4,800 locus sequence matrix of landfowl using target capture of ultraconserved elements. We then compared phylogenies estimated with concatenated maximum likelihood, quartet-based methods executed on concatenated matrices and gene tree reconciliation methods, across five thresholds of missing data. Results of maximum likelihood and quartet analyses were similar, well resolved, and demonstrated increasing support with increasing matrix size and sparseness. Conversely, gene tree reconciliation produced unexpected relationships when we included all informative loci, with certain taxa placed toward the root compared with other approaches. Inspection of these taxa identified a prevalence of short average contigs, which potentially biased gene tree inference and caused erroneous results in gene tree reconciliation. This suggests that the more problematic missing data in gene tree-based analyses are partial sequences rather than entire missing sequences from locus alignments. Limiting gene tree reconciliation to the most informative loci solved this problem, producing well-supported topologies congruent with concatenation and quartet methods. Collectively, our analyses provide a well-resolved phylogeny of landfowl, including strong support for previously problematic relationships such as those among junglefowl (Gallus), and clarify the position of two enigmatic galliform genera (Lerwa, Melanoperdix) not sampled in previous molecular phylogenetic studies.