diff --git a/.github/workflows/notify-coverage.yml b/.github/workflows/notify-coverage.yml
index c67b6a939..e176500a9 100644
--- a/.github/workflows/notify-coverage.yml
+++ b/.github/workflows/notify-coverage.yml
@@ -15,33 +15,98 @@ jobs:
     runs-on: ubuntu-latest
     outputs:
       msg: ${{ steps.make_msg.outputs.msg }}
+      should_notify: ${{ steps.get_coverage.outputs.should_notify }}
     steps:
+      - name: Download commit sha of the most recent successful run
+        uses: dawidd6/action-download-artifact@v2
+        with:
+          # Downloads the artifact from the most recent successful run
+          workflow: 'notify-coverage.yml'
+          name: head-sha.txt
+          if_no_artifact_found: ignore
       - name: Get today's and yesterday's coverage trends from codecov
+        id: get_coverage
         # API reference: https://docs.codecov.com/reference/repos_totals_retrieve
         run: |
-          YESTERDAY=$( date -u +%Y-%m-%dT%H:%M:%SZ -d 'yesterday' )
+          # Get the previous commit coverage, if the last sha is available
+          if [ ! -f head-sha.txt ]
+          then
+            echo "No previous coverage found."
 
+            # Update the head-sha.txt file with the current sha,
+            # so next time we campare against the current coverage.
+            echo ${{ github.sha }} > head-sha.txt
+
+            echo "should_notify=false"  >> "$GITHUB_OUTPUT"
+            exit 0
+          fi
+
+          PREV_SHA=$( cat head-sha.txt )
+          echo "Previous sha: \"$PREV_SHA\""
+
+          # Check if the sha has changed
+          if [ "$PREV_SHA" == "${{ github.sha }}" ]
+          then
+            echo "No new commits since last run."
+            echo "should_notify=false"  >> "$GITHUB_OUTPUT"
+            exit 0
+          fi
+
+          # Query the previous coverage from codecov
           curl --request GET \
-            --url "https://api.codecov.io/api/v2/github/${{ github.repository_owner }}/repos/${{ github.event.repository.name }}/coverage/?interval=1d&start_date=$YESTERDAY" \
+            --url "https://api.codecov.io/api/v2/github/${{ github.repository_owner }}/repos/${{ github.event.repository.name }}/totals/?sha=$PREV_SHA" \
             --header 'accept: application/json' \
             --header "authorization: Bearer ${{ secrets.CODECOV_GET_TOKEN }}" \
-            > coverage.json
-
-          echo "Coverage JSON:"
-          cat coverage.json
+            > coverage-prev.json
+          cat coverage-prev.json | jq ".totals.coverage" > coverage-prev.txt
+          echo "Previous coverage query result:"
+          cat coverage-prev.json | jq "del(.files)"
           echo
 
-          cat coverage.json | jq ".results[0].max" > coverage-prev.txt
-          cat coverage.json | jq ".results[-1].max" > coverage.txt
+          # Query the current coverage from codecov
+          curl --request GET \
+            --url "https://api.codecov.io/api/v2/github/${{ github.repository_owner }}/repos/${{ github.event.repository.name }}/totals/?sha=${{ github.sha }}" \
+            --header 'accept: application/json' \
+            --header "authorization: Bearer ${{ secrets.CODECOV_GET_TOKEN }}" \
+            > coverage.json
+          cat coverage.json | jq ".totals.coverage" > coverage.txt
+          echo "Current coverage query result:"
+          cat coverage.json | jq "del(.files)"
+          echo
 
+          echo
           echo "Previous coverage: `cat coverage-prev.txt`%"
           echo "Current coverage: `cat coverage.txt`%"
+
+          # A `null` in either coverage means that the coverage is not available,
+          # so we don't want to notify about that.
+          if [ "$( cat coverage-prev.txt )" == "null" ]
+          then
+            echo "Previous coverage not available."
+            echo ${{ github.sha }} > head-sha.txt
+            echo "should_notify=false"  >> "$GITHUB_OUTPUT"
+            exit 0
+          fi
+          if [ "$( cat coverage.txt )" == "null" ]
+          then
+            echo "Current coverage not available."
+            # Note that we don't update the head-sha.txt file here,
+            # so next time we compare against the one that had coverage data.
+            echo "should_notify=false"  >> "$GITHUB_OUTPUT"
+            exit 0
+          fi
+
+          echo ${{ github.sha }} > head-sha.txt
+          echo "should_notify=true"  >> "$GITHUB_OUTPUT"
       - name: Compare with previous summary and make message
         id: make_msg
+        if: steps.get_coverage.outputs.should_notify == 'true'
         run: |
-          change="`cat coverage-prev.txt`% --> `cat coverage.txt`%"
+          prev=`cat coverage-prev.txt`
+          current=`cat coverage-prev.txt`
+          change=`printf "%.2f%% --> %.2f%%" $prev $current`
           codecov="https://codecov.io/gh/${{ github.repository }}?search=&trend=7%20days"
-          if (( $(echo "`cat coverage-prev.txt` < `cat coverage.txt` + 0.04" | bc -l) ))
+          if (( $(echo "$prev < $current + 0.04" | bc -l) ))
           then
             MSG="msg=Coverage check for hugr shows no regression (${change}). ✅ ${codecov}"
           else
@@ -49,9 +114,16 @@ jobs:
           fi
           echo $MSG
           echo $MSG  >> "$GITHUB_OUTPUT"
+      - name: Upload current HEAD sha
+        uses: actions/upload-artifact@v3
+        with:
+          name: head-sha.txt
+          path: head-sha.txt
+
   notify-slack:
     needs: check-coverage
     runs-on: ubuntu-latest
+    if: needs.check-coverage.outputs.should_notify == 'true'
     steps:
       - name: Send notification
         uses: slackapi/slack-github-action@v1.24.0
@@ -60,4 +132,3 @@ jobs:
           slack-message: ${{ needs.check-coverage.outputs.msg }}
         env:
           SLACK_BOT_TOKEN: ${{ secrets.SLACK_BOT_TOKEN }}
-