diff --git a/CHANGES.md b/CHANGES.md
index 74a2e869..2efbe8e1 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -8,6 +8,7 @@
 * #321: Fix: For paired-end reads that cannot be placed as proper pairs, we now
   prefer placing them onto the same chrosome instead of on different ones if
   there is a choice.
+* #328: Adjust MAPQ computation for single-end reads.
 * #318: Added a `--details` option mainly intended for debugging. When used,
   some strobealign-specific tags are added to the SAM output that inform about
   things like no. of seeds found, whether mate rescue was performed etc.
diff --git a/src/aln.cpp b/src/aln.cpp
index aa392309..76350004 100644
--- a/src/aln.cpp
+++ b/src/aln.cpp
@@ -106,12 +106,11 @@ static inline void align_SE(
     Nam n_max = nams[0];
 
     int best_edit_distance = std::numeric_limits<int>::max();
-    int best_score = -1000;
+    int best_score = 0;
+    int second_best_score = 0;
 
     Alignment best_alignment;
-    best_alignment.score = -100000;
     best_alignment.is_unaligned = true;
-    int min_mapq_diff = best_edit_distance;
 
     for (auto &nam : nams) {
         float score_dropoff = (float) nam.n_hits / n_max.n_hits;
@@ -124,25 +123,25 @@ static inline void align_SE(
         details.tried_alignment++;
         details.gapped += alignment.gapped;
 
-        int diff_to_best = std::abs(best_score - alignment.score);
-        min_mapq_diff = std::min(min_mapq_diff, diff_to_best);
-
         if (max_secondary > 0) {
             alignments.emplace_back(alignment);
         }
         if (alignment.score > best_score) {
-            min_mapq_diff = std::max(0, alignment.score - best_score); // new distance to next best match
+            second_best_score = best_score;
             best_score = alignment.score;
             best_alignment = std::move(alignment);
             if (max_secondary == 0) {
                 best_edit_distance = best_alignment.global_ed;
             }
+        } else if (alignment.score > second_best_score) {
+            second_best_score = alignment.score;
         }
         tries++;
     }
+    uint8_t mapq = (60.0 * (best_score - second_best_score) + best_score - 1) / best_score;
+
     if (max_secondary == 0) {
-        best_alignment.mapq = std::min(min_mapq_diff, 60);
-        sam.add(best_alignment, record, read.rc, true, details);
+        sam.add(best_alignment, record, read.rc, mapq, true, details);
         return;
     }
     // Sort alignments by score, highest first
@@ -159,12 +158,7 @@ static inline void align_SE(
             break;
         }
         bool is_primary = i == 0;
-        if (is_primary) {
-            alignment.mapq = std::min(min_mapq_diff, 60);
-        } else {
-            alignment.mapq = 255;
-        }
-        sam.add(alignment, record, read.rc, is_primary, details);
+        sam.add(alignment, record, read.rc, mapq, is_primary, details);
     }
 }
 
diff --git a/src/sam.cpp b/src/sam.cpp
index 962ff9ce..0fb5a272 100644
--- a/src/sam.cpp
+++ b/src/sam.cpp
@@ -120,6 +120,7 @@ void Sam::add(
     const Alignment& alignment,
     const KSeq& record,
     const std::string& sequence_rc,
+    uint8_t mapq,
     bool is_primary,
     const Details& details
 ) {
@@ -131,8 +132,9 @@ void Sam::add(
     }
     if (!is_primary) {
         flags |= SECONDARY;
+        mapq = 255;
     }
-    add_record(record.name, flags, references.names[alignment.ref_id], alignment.ref_start, alignment.mapq, alignment.cigar, "*", -1, 0, record.seq, sequence_rc, record.qual, alignment.edit_distance, alignment.score, details);
+    add_record(record.name, flags, references.names[alignment.ref_id], alignment.ref_start, mapq, alignment.cigar, "*", -1, 0, record.seq, sequence_rc, record.qual, alignment.edit_distance, alignment.score, details);
 }
 
 // Add one individual record
diff --git a/src/sam.hpp b/src/sam.hpp
index c214dac4..ae9fb62a 100644
--- a/src/sam.hpp
+++ b/src/sam.hpp
@@ -15,7 +15,6 @@ struct Alignment {
     int edit_distance;
     int global_ed;
     int score;
-    uint8_t mapq;
     int length;
     bool is_rc;
     bool is_unaligned{false};
@@ -79,7 +78,7 @@ class Sam {
         }
 
     /* Add an alignment */
-    void add(const Alignment& alignment, const klibpp::KSeq& record, const std::string& sequence_rc, bool is_primary, const Details& details);
+    void add(const Alignment& alignment, const klibpp::KSeq& record, const std::string& sequence_rc, uint8_t mapq, bool is_primary, const Details& details);
     void add_pair(const Alignment& alignment1, const Alignment& alignment2, const klibpp::KSeq& record1, const klibpp::KSeq& record2, const std::string& read1_rc, const std::string& read2_rc, uint8_t mapq1, uint8_t mapq2, bool is_proper, bool is_primary, const std::array<Details, 2>& details);
     void add_unmapped(const klibpp::KSeq& record, uint16_t flags = UNMAP);
     void add_unmapped_pair(const klibpp::KSeq& r1, const klibpp::KSeq& r2);
diff --git a/tests/test_sam.cpp b/tests/test_sam.cpp
index b54a195d..d023d699 100644
--- a/tests/test_sam.cpp
+++ b/tests/test_sam.cpp
@@ -52,7 +52,6 @@ TEST_CASE("Sam::add") {
     aln.ref_start = 2;
     aln.edit_distance = 3;
     aln.score = 9;
-    aln.mapq = 55;
     aln.cigar = Cigar("2S2=1X3=3S");
 
     std::string read_rc = reverse_complement(record.seq);
@@ -61,7 +60,7 @@ TEST_CASE("Sam::add") {
     SUBCASE("Cigar =/X") {
         std::string sam_string;
         Sam sam(sam_string, references);
-        sam.add(aln, record, read_rc, is_primary, details);
+        sam.add(aln, record, read_rc, 55, is_primary, details);
         CHECK(sam_string ==
             "readname\t16\tcontig1\t3\t55\t2S2=1X3=3S\t*\t0\t0\tACGTT\tBB#>\tNM:i:3\tAS:i:9\n"
         );
@@ -69,7 +68,7 @@ TEST_CASE("Sam::add") {
     SUBCASE("Cigar M") {
         std::string sam_string;
         Sam sam(sam_string, references, CigarOps::M);
-        sam.add(aln, record, read_rc, is_primary, details);
+        sam.add(aln, record, read_rc, 55, is_primary, details);
         CHECK(sam_string ==
             "readname\t16\tcontig1\t3\t55\t2S6M3S\t*\t0\t0\tACGTT\tBB#>\tNM:i:3\tAS:i:9\n"
         );