Circadian clocks are endogenous oscillators driving daily rhythms in physiology. The cell-autonomous clock is governed by an interlocked network of transcriptional feedback loops. Hundreds of clock-controlled genes (CCGs) regulate tissue specific functions. Transcriptome studies reveal that different organs (e.g. liver, heart, adrenal gland) feature substantially varying sets of CCGs with different peak phase distributions. To study the phase variability of CCGs in mammalian peripheral tissues, we develop a core clock model for mouse liver and adrenal gland based on expression profiles and known cis-regulatory sites. 'Modulation factors' associated with E-boxes, ROR-elements, and D-boxes can explain variable rhythms of CCGs, which is demonstrated for differential regulation of cytochromes P450 and 12 h harmonics. By varying model parameters we explore how tissue-specific peak phase distributions can be generated. The central role of E-boxes and ROR-elements is confirmed by analysing ChIP-seq data of BMAL1 and REV-ERB transcription factors.