diff --git a/R/rmarkdown.R b/R/rmarkdown.R
index 5f0122505..d8641d986 100644
--- a/R/rmarkdown.R
+++ b/R/rmarkdown.R
@@ -56,8 +56,7 @@ render_rmarkdown <- function(pkg, input, output, ..., seed = NULL, copy_images =
     update_html(
       path,
       tweak_rmarkdown_html,
-      output_dir = path_dir(output_path),
-      input_dir = path_dir(input_path),
+      input_path = path_dir(input_path),
       pkg = pkg
     )
   }
diff --git a/R/tweak-page.R b/R/tweak-page.R
index c7ed6c13e..1deecea4f 100644
--- a/R/tweak-page.R
+++ b/R/tweak-page.R
@@ -37,38 +37,19 @@ tweak_page <- function(html, name, pkg = list(bs_version = 3)) {
   }
 }
 
-tweak_rmarkdown_html <- function(html, input_dir, output_dir, pkg = list(bs_version = 3)) {
+tweak_rmarkdown_html <- function(html, input_path, pkg = list(bs_version = 3)) {
   # Tweak classes of navbar
   toc <- xml2::xml_find_all(html, ".//div[@id='tocnav']//ul")
   xml2::xml_attr(toc, "class") <- "nav nav-pills nav-stacked"
 
+  # Make sure all images use relative paths
   img <- xml2::xml_find_all(html, "//img")
   src <- xml2::xml_attr(img, "src")
-
-  # Drop the logo and any inline images
-  is_ok <- !grepl("^data:", src) & xml2::xml_attr(img, "class", default = "") != "logo"
-  img <- img[is_ok]
-  src <- src[is_ok]
-
-  # Fix up absoluate paths to be relative to input_dir
   abs_src <- is_absolute_path(src)
   if (any(abs_src)) {
     purrr::walk2(
       img[abs_src],
-      path_rel(src[abs_src], input_dir),
-      xml2::xml_set_attr,
-      attr = "src"
-    )
-  }
-
-  # Fix up paths that are relative to input_dir instead of output_dir
-  output_dir <- path_real(output_dir)
-  input_abs_path <- purrr::map_chr(src, ~ path_abs(., input_dir))
-  up_path <- !abs_src & path_has_parent(input_abs_path, output_dir)
-  if (any(up_path)) {
-    purrr::walk2(
-      img[up_path],
-      path_rel(path_abs(src[up_path], input_dir), output_dir),
+      path_rel(src[abs_src], input_path),
       xml2::xml_set_attr,
       attr = "src"
     )
diff --git a/tests/testthat/test-tweak-page.R b/tests/testthat/test-tweak-page.R
index fe8c3fbeb..5db30340c 100644
--- a/tests/testthat/test-tweak-page.R
+++ b/tests/testthat/test-tweak-page.R
@@ -125,7 +125,7 @@ test_that("h1 section headings adjusted to h2 (and so on)", {
       <h1>2</h1>
     </div>
   ")
-  tweak_rmarkdown_html(html, input_dir = ".", output_dir = ".")
+  tweak_rmarkdown_html(html)
   expect_equal(xpath_text(html, ".//h1"), "Title")
   expect_equal(xpath_text(html, ".//h2"), c("1", "2"))
   expect_equal(xpath_text(html, ".//h3"), "1.1")