diff --git a/coverage_comment/main.py b/coverage_comment/main.py
index a354d6e3..513edbc3 100644
--- a/coverage_comment/main.py
+++ b/coverage_comment/main.py
@@ -119,11 +119,21 @@ def process_pr(
         base_ref=base_ref, coverage_path=config.COVERAGE_PATH
     )
 
-    previous_coverage_data_file = storage.get_datafile_contents(
-        github=gh,
-        repository=config.GITHUB_REPOSITORY,
-        branch=config.COVERAGE_DATA_BRANCH,
-    )
+    # It only really makes sense to display a comparison with the previous
+    # coverage if the PR target is the branch in which the coverage data is
+    # stored, e.g. the default branch.
+    # In the case we're running on a branch without a PR yet, we can't know
+    # if it's going to target the default branch, so we display it.
+    previous_coverage_data_file = None
+    pr_targets_default_branch = base_ref == repo_info.default_branch
+
+    if pr_targets_default_branch:
+        previous_coverage_data_file = storage.get_datafile_contents(
+            github=gh,
+            repository=config.GITHUB_REPOSITORY,
+            branch=config.COVERAGE_DATA_BRANCH,
+        )
+
     previous_coverage = None
     if previous_coverage_data_file:
         previous_coverage = files.parse_datafile(contents=previous_coverage_data_file)
@@ -135,6 +145,7 @@ def process_pr(
             previous_coverage_rate=previous_coverage,
             base_template=template.read_template_file("comment.md.j2"),
             custom_template=config.COMMENT_TEMPLATE,
+            pr_targets_default_branch=pr_targets_default_branch,
         )
     except template.MissingMarker:
         log.error(
diff --git a/coverage_comment/template.py b/coverage_comment/template.py
index 8cf83381..f212204d 100644
--- a/coverage_comment/template.py
+++ b/coverage_comment/template.py
@@ -45,6 +45,7 @@ def get_comment_markdown(
     previous_coverage_rate: decimal.Decimal | None,
     base_template: str,
     custom_template: str | None = None,
+    pr_targets_default_branch: bool = True,
 ):
     loader = CommentLoader(base_template=base_template, custom_template=custom_template)
     env = SandboxedEnvironment(loader=loader)
@@ -56,6 +57,7 @@ def get_comment_markdown(
             coverage=coverage,
             diff_coverage=diff_coverage,
             marker=MARKER,
+            pr_targets_default_branch=pr_targets_default_branch,
         )
     except jinja2.exceptions.TemplateError as exc:
         raise TemplateError from exc
diff --git a/coverage_comment/template_files/comment.md.j2 b/coverage_comment/template_files/comment.md.j2
index 95543145..1151d57c 100644
--- a/coverage_comment/template_files/comment.md.j2
+++ b/coverage_comment/template_files/comment.md.j2
@@ -15,8 +15,20 @@ The coverage rate went from `{{ previous_coverage_rate | pct }}` to `{{ coverage
 {%- endblock emoji_coverage -%}
 {%- else -%}
 {% block no_comparison_info -%}
-> **Note**
-> No coverage data of the default branch was found for comparison. A possible reason for this is that the coverage action has not yet run after a push event and the data is therefore not yet initialized.
+{%- if pr_targets_default_branch -%}
+{% block no_comparison_info_data_not_found_message -%}
+> [!NOTE]
+> Coverage data for the default branch was not found.
+> This usually happens when the action has not run on the default
+> branch yet, for example right after deploying it into the workflows.
+{%- endblock no_comparison_info_data_not_found_message -%}
+{% else %}
+{% block no_comparison_info_non_default_target -%}
+> [!NOTE]
+> Coverage evolution disabled because this PR targets a different branch
+> than the default branch, for which coverage data is not available.
+{%- endblock no_comparison_info_non_default_target -%}
+{% endif %}
 {%- endblock no_comparison_info %}
 
 {% block coverage_value_wording -%}