diff --git a/src/oidcc_backoff.erl b/src/oidcc_backoff.erl
index ccfc386..ed75bd0 100644
--- a/src/oidcc_backoff.erl
+++ b/src/oidcc_backoff.erl
@@ -48,11 +48,11 @@ priv_handle_retry(exponential, _Min, Max, State) ->
     {Wait, Wait};
 priv_handle_retry(random_exponential, Min, Max, undefined) ->
     Lower = max(Min, Max div 3),
-    priv_handle_retry(random_exponential, Min, Max, {Lower, Lower});
+    priv_handle_retry(random_exponential, Min, Max, {Min, Lower});
 priv_handle_retry(random_exponential, _Min, Max, {Prev, Lower}) ->
     NextMin = min(Prev, Lower),
     NextMax = min(Prev * 3, Max),
     Next = rand(NextMin, NextMax),
-    priv_handle_retry(random, NextMin, NextMax, {Next, Lower}).
+    {Next, {Next, Lower}}.
 
 rand(Min, Max) -> rand:uniform(Max - Min + 1) + Min - 1.
diff --git a/test/oidcc_backoff_test.erl b/test/oidcc_backoff_test.erl
index 9cb0a96..edcc689 100644
--- a/test/oidcc_backoff_test.erl
+++ b/test/oidcc_backoff_test.erl
@@ -84,6 +84,18 @@ rand_exp_backoff_in_min_max_test() ->
         calculate_backoffs(20, random_exponential, Min, Max)
     ).
 
+rand_exp_backoff_starts_near_min_test() ->
+    Min = 1000,
+    Max = 30000,
+    lists:foreach(
+        fun(_) ->
+            [{wait, Wait} | _] = calculate_backoffs(1, random_exponential, Min, Max),
+            ?assert(Wait >= Min),
+            ?assert(Wait =< Min * 3)
+        end,
+        lists:seq(1, 100)
+    ).
+
 rand_exp_backoff_increase_until_third_max_test() ->
     Min = 1000,
     Max = 30000,