diff --git a/crates/epaint/src/text/text_layout.rs b/crates/epaint/src/text/text_layout.rs
index b3e6953015d..4fa3ba49427 100644
--- a/crates/epaint/src/text/text_layout.rs
+++ b/crates/epaint/src/text/text_layout.rs
@@ -220,7 +220,7 @@ fn rows_from_paragraphs(
             });
         } else {
             let paragraph_max_x = paragraph.glyphs.last().unwrap().max_x();
-            if paragraph_max_x <= job.wrap.max_width {
+            if paragraph_max_x <= job.effective_wrap_width() {
                 // Early-out optimization: the whole paragraph fits on one row.
                 let paragraph_min_x = paragraph.glyphs[0].pos.x;
                 rows.push(Row {
@@ -241,11 +241,7 @@ fn rows_from_paragraphs(
 }
 
 fn line_break(paragraph: &Paragraph, job: &LayoutJob, out_rows: &mut Vec<Row>, elided: &mut bool) {
-    let wrap_width_margin = if job.round_output_size_to_nearest_ui_point {
-        0.5
-    } else {
-        0.0
-    };
+    let wrap_width = job.effective_wrap_width();
 
     // Keeps track of good places to insert row break if we exceed `wrap_width`.
     let mut row_break_candidates = RowBreakCandidates::default();
@@ -262,7 +258,7 @@ fn line_break(paragraph: &Paragraph, job: &LayoutJob, out_rows: &mut Vec<Row>, e
 
         let potential_row_width = paragraph.glyphs[i].max_x() - row_start_x;
 
-        if job.wrap.max_width + wrap_width_margin < potential_row_width {
+        if wrap_width < potential_row_width {
             // Row break:
 
             if first_row_indentation > 0.0
@@ -420,7 +416,7 @@ fn replace_last_glyph_with_overflow_character(
         });
     }
 
-    if row_width(row) <= job.wrap.max_width || row.glyphs.len() == 1 {
+    if row_width(row) <= job.effective_wrap_width() || row.glyphs.len() == 1 {
         return; // we are done
     }
 
@@ -467,7 +463,7 @@ fn replace_last_glyph_with_overflow_character(
             }
 
             // Check if we're within width budget:
-            if row_width(row) <= job.wrap.max_width || row.glyphs.len() == 1 {
+            if row_width(row) <= job.effective_wrap_width() || row.glyphs.len() == 1 {
                 return; // We are done
             }
 
@@ -653,8 +649,8 @@ fn galley_from_rows(
             // If the user picked a too aggressive wrap width (e.g. more narrow than any individual glyph),
             // we should let the user know.
         } else {
-            // Make sure we don't over the max wrap width the user picked:
-            rect.max.x = rect.max.x.at_most(rect.min.x + job.wrap.max_width);
+            // Make sure we don't go over the max wrap width the user picked:
+            rect.max.x = rect.max.x.at_most(rect.min.x + job.wrap.max_width).floor();
         }
     }
 
diff --git a/crates/epaint/src/text/text_layout_types.rs b/crates/epaint/src/text/text_layout_types.rs
index c754061b5f2..df20c63c31d 100644
--- a/crates/epaint/src/text/text_layout_types.rs
+++ b/crates/epaint/src/text/text_layout_types.rs
@@ -175,6 +175,18 @@ impl LayoutJob {
         }
         max_height
     }
+
+    /// The wrap with, with a small margin in some cases.
+    pub fn effective_wrap_width(&self) -> f32 {
+        if self.round_output_size_to_nearest_ui_point {
+            // On a previous pass we may have rounded down by at most 0.5 and reported that as a width.
+            // egui may then set that width as the max width for subsequent frames, and it is important
+            // that we then don't wrap earlier.
+            self.wrap.max_width + 0.5
+        } else {
+            self.wrap.max_width
+        }
+    }
 }
 
 impl std::hash::Hash for LayoutJob {