diff --git a/NEWS.md b/NEWS.md
index 87eaa55d..81bbc7dd 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -12,6 +12,9 @@
 
 * `copyDependencyToDir()` no longer creates empty directories for dependencies that do not have any files. (@gadenbuie, #276)
 
+* Closed #320: `copyDependencyToDir()` now works with dependencies
+with specified attributes.  (@dmurdoch, #321)
+
 # htmltools 0.5.2
 
 ## Breaking Changes
diff --git a/R/html_dependency.R b/R/html_dependency.R
index 662a323c..7b393ba8 100644
--- a/R/html_dependency.R
+++ b/R/html_dependency.R
@@ -354,9 +354,12 @@ copyDependencyToDir <- function(dependency, outputDir, mustWork = TRUE) {
   dir.create(target_dir)
   dependency$src$file <- normalizePath(target_dir, "/", TRUE)
 
-  files <- if (dependency$all_files) list.files(dir) else {
-    unlist(dependency[c('script', 'stylesheet', 'attachment')])
-  }
+  if (dependency$all_files)
+    files <- list.files(dir)
+  else
+    files <- c(pluck_src(dependency$script),
+               pluck_src(dependency$stylesheet),
+               pluck_src(dependency$attachment))
 
   if (length(files) == 0) {
     # This dependency doesn't include any files
@@ -366,11 +369,12 @@ copyDependencyToDir <- function(dependency, outputDir, mustWork = TRUE) {
   }
 
   srcfiles <- file.path(dir, files)
-  if (any(!file.exists(srcfiles))) {
+  missing_srcfiles <- !file.exists(srcfiles)
+  if (any(missing_srcfiles)) {
     stop(
       sprintf(
         "Can't copy dependency files that don't exist: '%s'",
-        paste(srcfiles, collapse = "', '")
+        paste(srcfiles[missing_srcfiles], collapse = "', '")
       )
     )
   }
diff --git a/R/utils.R b/R/utils.R
index c72ae1f1..493e0afc 100644
--- a/R/utils.R
+++ b/R/utils.R
@@ -151,3 +151,12 @@ anyUnnamed <- function(x) {
   # List with name attribute; check for any ""
   any(!nzchar(nms))
 }
+
+# Get the source filename out of a script or similar
+# entry.
+pluck_src <- function(x) {
+  if (is.character(x)) return(x)
+  if (is.list(x) && "src" %in% names(x)) return(x$src)
+  if (is.list(x)) return(vapply(x, pluck_src, ""))
+  NULL
+}
diff --git a/tests/testthat/test-deps.r b/tests/testthat/test-deps.r
index eef577ce..b6337ef2 100644
--- a/tests/testthat/test-deps.r
+++ b/tests/testthat/test-deps.r
@@ -357,3 +357,90 @@ test_that("copyDependencyToDir() doesn't create an empty directory", {
   # to keep relativeTo() from throwing an error later in Rmd render process
   expect_match(copied_dep$src$file, normalizePath(tmp_rmd, "/", TRUE), fixed = TRUE)
 })
+
+test_that("copyDependencyToDir() handles attributes", {
+  tmp_dep <- tempfile("dep")
+  dir.create(tmp_dep)
+  on.exit(unlink(tmp_dep))
+
+  tmp_txt <- "temp.txt"
+  path <- file.path(tmp_dep, tmp_txt)
+  writeLines("Some text in the text/plain dep", path)
+
+  tmp_js <- "javascript.js"
+  path <- file.path(tmp_dep, tmp_js)
+  writeLines('console.log("log message");', path)
+
+  tmp_rmd <- tempfile("rmd_files")
+  dir.create(tmp_rmd)
+  on.exit(unlink(tmp_rmd), add = TRUE)
+
+  dep_with_attributes <- htmltools::htmlDependency(
+    name = "textPlain",
+    version = "9.9.9",
+    src = tmp_dep,
+    script = list(src = tmp_txt, type = "text/plain"),
+    all_files = FALSE
+  )
+
+  dep_without <- htmltools::htmlDependency(
+    name = "textPlain",
+    version = "9.9.9",
+    src = tmp_dep,
+    script = tmp_js,
+    all_files = FALSE
+  )
+
+  dep_with_both <- htmltools::htmlDependency(
+    name = "textPlain",
+    version = "9.9.9",
+    src = tmp_dep,
+    script = list(tmp_js,
+                  list(src = tmp_txt, type = "text/plain")),
+    all_files = FALSE
+  )
+
+  dep_with_one_nested <- htmltools::htmlDependency(
+    name = "textPlain",
+    version = "9.9.9",
+    src = tmp_dep,
+    script = list(list(src = tmp_txt, type = "text/plain")),
+    all_files = FALSE
+  )
+
+  dep_with_missings <- htmltools::htmlDependency(
+    name = "textPlain",
+    version = "9.9.9",
+    src = tmp_dep,
+    script = list(tmp_js,
+                  "foobar1",
+                  list(src = "foobar2")),
+    all_files = FALSE
+  )
+
+  # None of these except the last should trigger errors as
+  # the first two did in issue #320
+
+  copyDependencyToDir(dep_with_attributes, tmp_rmd)
+  expect_equal(dir(tmp_rmd, recursive = TRUE),
+               "textPlain-9.9.9/temp.txt")
+
+  unlink(dir(tmp_rmd, recursive = TRUE))
+  copyDependencyToDir(dep_with_both, tmp_rmd)
+  expect_equal(dir(tmp_rmd, recursive = TRUE),
+               c("textPlain-9.9.9/javascript.js",
+                 "textPlain-9.9.9/temp.txt"))
+
+  unlink(dir(tmp_rmd, recursive = TRUE))
+  copyDependencyToDir(dep_without, tmp_rmd)
+  expect_equal(dir(tmp_rmd, recursive = TRUE),
+               "textPlain-9.9.9/javascript.js")
+
+  unlink(dir(tmp_rmd, recursive = TRUE))
+  copyDependencyToDir(dep_with_one_nested, tmp_rmd)
+  expect_equal(dir(tmp_rmd, recursive = TRUE),
+               "textPlain-9.9.9/temp.txt")
+
+  expect_error(copyDependencyToDir(dep_with_missings, tmp_rmd))
+
+})