diff --git a/lib/postal/message_db/message.rb b/lib/postal/message_db/message.rb
index 0fc7fcc..d3783d8 100644
--- a/lib/postal/message_db/message.rb
+++ b/lib/postal/message_db/message.rb
@@ -329,6 +329,8 @@ module Postal
           mail.header.fields.each_with_object({}) do |field, hash|
             hash[field.name.downcase] ||= []
             hash[field.name.downcase] << field.decoded
+          rescue Mail::Field::IncompleteParseError
+            # Never mind, move on to the next header
           end
         end
       end