diff --git a/src/main/scala/com/fulcrumgenomics/umi/ConsensusCallingIterator.scala b/src/main/scala/com/fulcrumgenomics/umi/ConsensusCallingIterator.scala
index b5ab48065..5dba4cde7 100644
--- a/src/main/scala/com/fulcrumgenomics/umi/ConsensusCallingIterator.scala
+++ b/src/main/scala/com/fulcrumgenomics/umi/ConsensusCallingIterator.scala
@@ -53,13 +53,12 @@ class ConsensusCallingIterator[ConsensusRead <: SimpleRead](sourceIterator: Iter
   private var collectedStats: Boolean = false
 
   protected val iter: Iterator[SamRecord] = {
-    // Only mapped reads may contribute to a consensus.  An unmapped read has no cigar, and an empty cigar is a prefix
-    // of every cigar, so `filterToMostCommonAlignment` would match it against whichever alignment group it was tested
-    // against first rather than rejecting it as a minority alignment.  Note that the mapped end of a half-mapped pair
-    // is still used; only the unmapped end is dropped.
+    // Templates with no mapped read at all are dropped here; the unmapped end of a half-mapped pair is passed through
+    // to the caller, which rejects it as `RejectionReason.Unmapped` so that it is counted and written to the rejects
+    // output rather than silently discarded.
     val filteredIterator = sourceIterator
       .filterNot (r => r.secondary || r.supplementary)
-      .filter(r => r.mapped)
+      .filter(r => r.mapped || (r.paired && r.mateMapped))
 
     // Wrap our input iterator in a progress logging iterator if we have a progress logger
     val progressIterator = progress match {
diff --git a/src/main/scala/com/fulcrumgenomics/umi/UmiConsensusCaller.scala b/src/main/scala/com/fulcrumgenomics/umi/UmiConsensusCaller.scala
index 9d61fae27..8dc460866 100644
--- a/src/main/scala/com/fulcrumgenomics/umi/UmiConsensusCaller.scala
+++ b/src/main/scala/com/fulcrumgenomics/umi/UmiConsensusCaller.scala
@@ -86,6 +86,7 @@ object UmiConsensusCaller {
     case object HighDuplexDisagreement   extends _RejectionReason("high_duplex_disagreement",    "Too many errors between top/bottoms strands", false, false, true)
     case object ClipOverlapFailed        extends _RejectionReason("clip_overlap_failed",         "See https://github.com/fulcrumgenomics/fgbio/issues/1090", false, false, true)
     case object NotPrimaryFrPair         extends _RejectionReason("not_primary_fr_pair",         "Template did not have a single primary FR pair of reads", false, false, true)
+    case object Unmapped                 extends _RejectionReason("unmapped",                    "Read is unmapped", true, true, true)
   }
 
   /** Metric class for outputting consensus calling statistics. */
@@ -351,10 +352,18 @@ trait UmiConsensusCaller[ConsensusRead <: SimpleRead] {
     */
   final def consensusReadsFromSamRecords(recs: Seq[SamRecord]): Seq[SamRecord] = {
     this._totalReads += recs.size
+
+    // Unmapped reads cannot contribute to a consensus: they have no cigar, and an empty cigar is a prefix of every
+    // cigar, so `filterToMostCommonAlignment` would match one against whichever alignment group it was tested against
+    // first rather than rejecting it.  Rejecting here rather than filtering upstream keeps them visible in the rejects
+    // output and in the rejection counts.  The mapped end of a half-mapped pair is unaffected.
+    val (mapped, unmapped) = recs.partition(_.mapped)
+    if (unmapped.nonEmpty) rejectRecords(unmapped, RejectionReason.Unmapped)
+
     // Ensure that mate cigar is set on all read pairs.  This is needed when using
     // `clipper.numBasesExtendingPastMate` subsequently
-    updateMateCigars(recs)
-    val result = consensusSamRecordsFromSamRecords(recs)
+    updateMateCigars(mapped)
+    val result = consensusSamRecordsFromSamRecords(mapped)
     this._consensusReadsConstructed += result.size
     result
   }
diff --git a/src/test/scala/com/fulcrumgenomics/umi/CallMolecularConsensusReadsTest.scala b/src/test/scala/com/fulcrumgenomics/umi/CallMolecularConsensusReadsTest.scala
index 76620ebac..bac08c6af 100644
--- a/src/test/scala/com/fulcrumgenomics/umi/CallMolecularConsensusReadsTest.scala
+++ b/src/test/scala/com/fulcrumgenomics/umi/CallMolecularConsensusReadsTest.scala
@@ -27,6 +27,8 @@ package com.fulcrumgenomics.umi
 
 import com.fulcrumgenomics.bam.api.SamOrder
 import com.fulcrumgenomics.testing.{SamBuilder, UnitSpec}
+import com.fulcrumgenomics.umi.UmiConsensusCaller.{ConsensusKvMetric, RejectionReason}
+import com.fulcrumgenomics.util.Metric
 import com.fulcrumgenomics.umi.VanillaUmiConsensusCallerOptions._
 
 /**
@@ -131,6 +133,7 @@ class CallMolecularConsensusReadsTest extends UnitSpec {
       val rlen    = 100
       val output  = newBam
       val rejects = newBam
+      val stats   = makeTempFile("call_molecular_consensus_reads_test.", ".txt")
 
       new CallMolecularConsensusReads(
         input       = halfMappedFamily(rlen).toTempFile(),
@@ -138,6 +141,7 @@ class CallMolecularConsensusReadsTest extends UnitSpec {
         minReads    = 1,
         maxReads    = Some(maxReads),
         rejects     = Some(rejects),
+        stats       = Some(stats),
         readGroupId = "ABC"
       ).execute()
 
@@ -156,8 +160,14 @@ class CallMolecularConsensusReadsTest extends UnitSpec {
       r2[Int](ConsensusTags.PerRead.RawReadCount) shouldBe 2
       r2.basesString shouldBe "C" * rlen
 
-      // The unmapped R2 must not have been used, whether it was rejected by the caller or filtered before reaching it.
-      readBamRecs(rejects).foreach { rec => rec.name shouldBe "halfmapped:3" }
+      // The unmapped R2 must not have been used, and must be accounted for rather than vanishing:
+      // it is written to the rejects BAM and counted under its own rejection reason.
+      val rejected = readBamRecs(rejects)
+      rejected.map(rec => (rec.name, rec.secondOfPair)) should contain theSameElementsAs Seq(("halfmapped:3", true))
+
+      val metrics = Metric.read[ConsensusKvMetric](stats).map(m => m.key -> m.value.toString).toMap
+      metrics(s"raw_reads_rejected_for_${RejectionReason.Unmapped.code}") shouldBe "1"
+      metrics("raw_reads_considered") shouldBe "6"
     }
   }
 }