diff --git a/CHANGELOG.md b/CHANGELOG.md
index 8cecb229d8..ab7e26a93b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -78,6 +78,12 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
   to-be-pushed commit has conflicts, or has no description / committer / author
   set. [#3029](https://github.com/martinvonz/jj/issues/3029)
 
+* Conflicts involving non-empty files that do not end in a newline no longer
+  look broken when materialized.
+  [#3968](https://github.com/martinvonz/jj/issues/3968). This is a partial fix,
+  see also [#3975](https://github.com/martinvonz/jj/issues/3968) which is not
+  yet fixed.
+
 ## [0.18.0] - 2024-06-05
 
 ### Breaking changes
diff --git a/lib/src/conflicts.rs b/lib/src/conflicts.rs
index 9d6ff0212f..097de8a48a 100644
--- a/lib/src/conflicts.rs
+++ b/lib/src/conflicts.rs
@@ -53,6 +53,8 @@ static CONFLICT_MARKER_REGEX: once_cell::sync::Lazy<Regex> = once_cell::sync::La
     .unwrap()
 });
 
+/// This function assumes that each hunk consists of 0 or more lines, each
+/// ending with a newline.
 fn write_diff_hunks(hunks: &[DiffHunk], file: &mut dyn Write) -> std::io::Result<()> {
     for hunk in hunks {
         match hunk {
@@ -218,6 +220,16 @@ pub fn materialize_merge_result(
     single_hunk: Merge<ContentHunk>,
     output: &mut dyn Write,
 ) -> std::io::Result<()> {
+    // The following code assumes that each version of the file contains 0 or
+    // more lines, each ending with `\n`. For now, we force this to be true.
+    // TODO(#3795): A better solution for this.
+    let single_hunk: Merge<ContentHunk> = single_hunk.into_map(|ContentHunk(mut side)| {
+        if !side.is_empty() && !side.ends_with(b"\n") {
+            side.push(b'\n');
+        };
+        ContentHunk(side)
+    });
+
     let slices = single_hunk.map(|content| content.0.as_slice());
     let merge_result = files::merge(&slices);
     match merge_result {
@@ -239,6 +251,7 @@ pub fn materialize_merge_result(
                     output.write_all(
                         format!(" Conflict {conflict_index} of {num_conflicts}\n").as_bytes(),
                     )?;
+
                     let mut add_index = 0;
                     for (base_index, left) in hunk.removes().enumerate() {
                         // The vast majority of conflicts one actually tries to
diff --git a/lib/src/merge.rs b/lib/src/merge.rs
index e16786ee36..0eef5a45ea 100644
--- a/lib/src/merge.rs
+++ b/lib/src/merge.rs
@@ -345,6 +345,12 @@ impl<T> Merge<T> {
         self.values.iter_mut()
     }
 
+    /// Creates a new merge by applying `f` to each remove and add.
+    pub fn into_map<U>(self, f: impl FnMut(T) -> U) -> Merge<U> {
+        let values = self.values.into_iter().map(f).collect();
+        Merge { values }
+    }
+
     /// Creates a new merge by applying `f` to each remove and add.
     pub fn map<'a, U>(&'a self, f: impl FnMut(&'a T) -> U) -> Merge<U> {
         let values = self.values.iter().map(f).collect();
diff --git a/lib/tests/test_conflicts.rs b/lib/tests/test_conflicts.rs
index 4d7ee7d790..d24b760fd7 100644
--- a/lib/tests/test_conflicts.rs
+++ b/lib/tests/test_conflicts.rs
@@ -357,15 +357,31 @@ fn test_materialize_conflict_no_newlines_at_eof() {
         @r###"
     <<<<<<< Conflict 1 of 1
     %%%%%%% Changes from base to side #1
-    -base+++++++ Contents of side #2
-    right>>>>>>> Conflict 1 of 1 ends
+    -base
+    +++++++ Contents of side #2
+    right
+    >>>>>>> Conflict 1 of 1 ends
     "###
     );
-    // BUG(#3968): These conflict markers cannot be parsed
+    // These conflict markers can be parsed (#3968)
+    // TODO(#3975): BUG: The result of the parsing has newlines where original files
+    // didn't.
     insta::assert_debug_snapshot!(parse_conflict(
         materialized.as_bytes(),
         conflict.num_sides()
-    ),@"None");
+    ),@r###"
+    Some(
+        [
+            Conflicted(
+                [
+                    "",
+                    "base\n",
+                    "right\n",
+                ],
+            ),
+        ],
+    )
+    "###);
 }
 
 #[test]