diff --git a/Library/Homebrew/dev-cmd/pull.rb b/Library/Homebrew/dev-cmd/pull.rb
index 1cc3231627..f9e3582b30 100644
--- a/Library/Homebrew/dev-cmd/pull.rb
+++ b/Library/Homebrew/dev-cmd/pull.rb
@@ -641,7 +641,7 @@ module Homebrew
         # We're in the cache; make sure to force re-download
         loop do
           begin
-            curl_download url, continue_at: 0, to: filename
+            curl_download url, to: filename
             break
           rescue
             if retry_count >= max_curl_retries
diff --git a/Library/Homebrew/test/download_strategies_spec.rb b/Library/Homebrew/test/download_strategies_spec.rb
index 012370b70e..71385c7f58 100644
--- a/Library/Homebrew/test/download_strategies_spec.rb
+++ b/Library/Homebrew/test/download_strategies_spec.rb
@@ -262,7 +262,7 @@ describe CurlDownloadStrategy do
       expect(subject).to receive(:curl).with(
         "--location",
         "--remote-time",
-        "--continue-at", "-",
+        "--continue-at", "0",
         "--output", an_instance_of(Pathname),
         url,
         an_instance_of(Hash)
diff --git a/Library/Homebrew/utils/curl.rb b/Library/Homebrew/utils/curl.rb
index 2856012bbe..40e8f26380 100644
--- a/Library/Homebrew/utils/curl.rb
+++ b/Library/Homebrew/utils/curl.rb
@@ -46,21 +46,20 @@ def curl(*args)
                   env: { "SSL_CERT_FILE" => nil }
 end
 
-def curl_download(*args, to: nil, continue_at: "-", **options)
+def curl_download(*args, to: nil, **options)
   destination = Pathname(to)
-  had_incomplete_download ||= destination.exist?
   destination.dirname.mkpath
-  curl("--location", "--remote-time", "--continue-at", continue_at.to_s, "--output", destination, *args, **options)
-rescue ErrorDuringExecution => e
-  # `curl` error 33: HTTP server doesn't seem to support byte ranges. Cannot resume.
-  # HTTP status 416: Requested range not satisfiable
-  if (e.status.exitstatus == 33 || had_incomplete_download) && continue_at == "-"
-    continue_at = 0
-    had_incomplete_download = false
-    retry
+
+  continue_at = if destination.exist? &&
+                   curl_output("--location", "--head", "--range", "0-1",
+                               "--write-out", "%{http_code}",
+                               "--output", "/dev/null", *args, **options).stdout.to_i == 206 # Partial Content
+    "-"
+  else
+    0
   end
 
-  raise
+  curl("--location", "--remote-time", "--continue-at", continue_at.to_s, "--output", destination, *args, **options)
 end
 
 def curl_output(*args, **options)