diff --git a/src/scroller_page.cpp b/src/scroller_page.cpp
index 4df2682..6483a54 100644
--- a/src/scroller_page.cpp
+++ b/src/scroller_page.cpp
@@ -140,26 +140,32 @@ void ScrollerPage::update(float dt)
 
     if (velocity_ > 0.0f)
     {
-        // Lines move downward; recycle the bottom line off-screen and add a new
-        // line just above the top.
-        ScrollerLine &back = lines_.back();
-        if (back.words[0].y > screenH_)
+        // Lines move downward. Recycle every line that scrolled fully off the
+        // bottom this frame (movement is continuous, so one frame can cover
+        // several line heights) and add a replacement just above the top.
+        while (!lines_.empty() && lines_.back().words[0].y > screenH_)
         {
             float baseY = lines_.front().words[0].y - lineHeight_;
             lines_.pop_back();
-            addLineAt(baseY);
+            if (!addLineAt(baseY))
+            {
+                break;
+            }
         }
     }
     else if (velocity_ < 0.0f)
     {
-        // Lines move upward; recycle the top line off-screen and add a new line
-        // just below the bottom.
-        ScrollerLine &front = lines_.front();
-        if (front.words[0].y + front.words[0].height < 0.0f)
+        // Lines move upward. Recycle every line that scrolled fully off the top
+        // this frame and add a replacement just below the bottom.
+        while (!lines_.empty() &&
+               lines_.front().words[0].y + lines_.front().words[0].height < 0.0f)
         {
             float baseY = lines_.back().words[0].y + lineHeight_;
             lines_.pop_front();
-            addLineAt(baseY);
+            if (!addLineAt(baseY))
+            {
+                break;
+            }
         }
     }
 }
@@ -380,18 +386,18 @@ void ScrollerPage::prefillLines()
     }
 }
 
-void ScrollerPage::addLineAt(float baseY)
+bool ScrollerPage::addLineAt(float baseY)
 {
     if (streams_.empty() || !font_)
     {
-        return;
+        return false;
     }
 
     ProclamationStream &stream = streams_[streamIndex_];
     if (stream.words.empty())
     {
         advanceStream();
-        return;
+        return false;
     }
 
     FibonacciLinePattern &pattern = patterns_[streamIndex_];
@@ -451,7 +457,7 @@ void ScrollerPage::addLineAt(float baseY)
 
     if (line.words.empty())
     {
-        return;
+        return false;
     }
     line.width = width;
 
@@ -471,6 +477,7 @@ void ScrollerPage::addLineAt(float baseY)
     {
         lines_.push_back(std::move(line));
     }
+    return true;
 }
 
 void ScrollerPage::advanceStream()
diff --git a/src/scroller_page.h b/src/scroller_page.h
index 01bbe5a..4160cae 100644
--- a/src/scroller_page.h
+++ b/src/scroller_page.h
@@ -79,7 +79,7 @@ private:
     void destroyResources();
     void rebuildWordTextures();
     void prefillLines();
-    void addLineAt(float baseY);
+    bool addLineAt(float baseY);
     void advanceStream();
     void switchAudioForCurrentStream();
     void updateAutoVelocity(float dt);