diff --git a/lua/md-render/preview.lua b/lua/md-render/preview.lua
index 0c35420..476430e 100644
--- a/lua/md-render/preview.lua
+++ b/lua/md-render/preview.lua
@@ -521,6 +521,10 @@ function Session:scroll_to_source_line(source_cursor_line)
   target = math.max(1, math.min(target, buf_lines))
   local win_height = vim.api.nvim_win_get_height(self.win)
   local top = math.max(0, target - 1 - math.floor(win_height / 2))
+  -- Centering must not scroll past the end: a document that fits the window
+  -- would lose its first lines and leave the bottom rows empty.  Each line
+  -- takes at least one row, so this still fills the window when lines wrap.
+  top = math.min(top, math.max(0, buf_lines - win_height))
   vim.api.nvim_win_call(self.win, function()
     vim.fn.winrestview { topline = top + 1 }
   end)
diff --git a/tests/preview_scroll_test.lua b/tests/preview_scroll_test.lua
new file mode 100644
index 0000000..2ef9ca5
--- /dev/null
+++ b/tests/preview_scroll_test.lua
@@ -0,0 +1,66 @@
+-- Test where the floating preview opens.  It centers the line under the
+-- source cursor, but must not scroll past the end: a document that fits the
+-- window shows from its first line.
+-- Run: nvim --headless -u NONE --noplugin -l tests/preview_scroll_test.lua
+
+package.path = vim.fn.getcwd() .. "/lua/?.lua;" .. vim.fn.getcwd() .. "/lua/?/init.lua;" .. package.path
+
+local preview = require "md-render.preview"
+
+local pass_count = 0
+local fail_count = 0
+
+local function assert_eq(actual, expected, msg)
+  if vim.deep_equal(actual, expected) then
+    pass_count = pass_count + 1
+  else
+    fail_count = fail_count + 1
+    print("FAIL: " .. msg)
+    print("  expected: " .. vim.inspect(expected))
+    print("  actual:   " .. vim.inspect(actual))
+  end
+end
+
+vim.o.lines, vim.o.columns = 40, 120
+
+--- Open the float on `lines` with the source cursor on `cursor_line`, and
+--- return the float's topline, height and line count.
+local function open(lines, cursor_line)
+  local path = vim.fn.tempname() .. ".md"
+  vim.fn.writefile(lines, path)
+  vim.cmd("edit " .. path)
+  vim.api.nvim_win_set_cursor(0, { cursor_line, 0 })
+  preview.show()
+  local win = vim.api.nvim_get_current_win()
+  local r = {
+    topline = vim.fn.line "w0",
+    height = vim.api.nvim_win_get_height(win),
+    lines = vim.api.nvim_buf_line_count(0),
+  }
+  vim.api.nvim_win_close(win, true)
+  vim.cmd "bwipeout!"
+  vim.fn.delete(path)
+  return r
+end
+
+-- Test 1: a short document starts at its first line, wherever the cursor is
+do
+  local r = open({ "## Heading", "", "One.", "", "Two.", "", "Three.", "", "Four." }, 9)
+  assert_eq(r.lines <= r.height, true, "the document should fit the float")
+  assert_eq(r.topline, 1, "a document that fits should not be scrolled")
+end
+
+-- Test 2: a long document still centers the cursor line
+do
+  local lines = {}
+  for i = 1, 200 do
+    table.insert(lines, ("Paragraph %d."):format(i))
+    table.insert(lines, "")
+  end
+  local r = open(lines, 199)
+  assert_eq(r.topline > 1, true, "the cursor line in the middle of a long document should be scrolled to")
+  assert_eq(r.topline <= r.lines - r.height + 1, true, "the last line should not leave empty rows below it")
+end
+
+print(string.format("\n%d passed, %d failed", pass_count, fail_count))
+if fail_count > 0 then os.exit(1) end