diff --git a/ChangeLog b/ChangeLog
index ec5d9ec8..18dc216c 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,9 @@
+2019-01-02  Jay Berkenbilt  <ejb@ql.org>
+
+	* Add method QPDFObjectHandle::getResourceNames that returns a set
+	of strings representing all second-level keys in a dictionary
+	(i.e. all keys of all direct dictionary members).
+
 2018-12-31  Jay Berkenbilt  <ejb@ql.org>
 
 	* Add methods for flattening form fields and annotations:
diff --git a/libqpdf/QPDFPageDocumentHelper.cc b/libqpdf/QPDFPageDocumentHelper.cc
index 7b171e9a..d168f8de 100644
--- a/libqpdf/QPDFPageDocumentHelper.cc
+++ b/libqpdf/QPDFPageDocumentHelper.cc
@@ -164,7 +164,8 @@ QPDFPageDocumentHelper::flattenAnnotationsForPage(
             }
             std::set<std::string> names = resources.getResourceNames();
             std::string name;
-            while (next_fx < 1000000)
+            int max_fx = next_fx + names.size() + 1;
+            while (next_fx <= max_fx)
             {
                 std::string candidate = "/Fxo" + QUtil::int_to_string(next_fx);
                 ++next_fx;
@@ -176,9 +177,9 @@ QPDFPageDocumentHelper::flattenAnnotationsForPage(
             }
             if (name.empty())
             {
-                // There are already more than a million /Fxo names.
-                // Somehow I doubt this is going to actually happen.
-                // Just pick a name and forget conflicts.
+                // This could only happen if there is a coding error.
+                // The number of candidates we test is more than the
+                // number of keys we're checking against.
                 name = "/FxConflict";
             }
             resources.mergeResources(