The plastid genomes of peridinin-containing dinoflagellates are highly unusual, possessing very few genes, which are located on small chromosomal elements termed "minicircles". These minicircles may contain genes, or no recognisable coding information. Transcripts produced from minicircles may undergo unusual processing events, such as the addition of a 3' poly(U) tail. To date, little is known about the genetic or transcriptional diversity of non-coding sequences in peridinin dinoflagellate plastids. These sequences include empty minicircles, and regions of non-coding DNA in coding minicircles. Here, we present an integrated plastid genome and transcriptome for the model peridinin dinoflagellate Amphidinium carterae, identifying a previously undescribed minicircle. We also profile transcripts covering non-coding regions of the psbA and petB/atpA minicircles. We present evidence that antisense transcripts are produced within the A. carterae plastid, but show that these transcripts undergo different end cleavage events from sense transcripts, and do not receive 3' poly(U) tails. The difference in processing events between sense and antisense transcripts may enable the removal of non-coding transcripts from peridinin dinoflagellate plastid transcript pools.