diff --git a/infer/src/absint/PatternMatch.ml b/infer/src/absint/PatternMatch.ml
index 561a8e9ca..986fc2a14 100644
--- a/infer/src/absint/PatternMatch.ml
+++ b/infer/src/absint/PatternMatch.ml
@@ -58,6 +58,8 @@ let implements_iterator = implements "java.util.Iterator"
 
 let implements_collection = implements "java.util.Collection"
 
+let implements_collections = implements "java.util.Collections"
+
 let implements_list = implements "java.util.List"
 
 let implements_pseudo_collection t s =
diff --git a/infer/src/absint/PatternMatch.mli b/infer/src/absint/PatternMatch.mli
index eeb81f2b5..09a0ba599 100644
--- a/infer/src/absint/PatternMatch.mli
+++ b/infer/src/absint/PatternMatch.mli
@@ -36,6 +36,9 @@ val implements_iterator : Tenv.t -> string -> bool
 val implements_collection : Tenv.t -> string -> bool
 (** Check whether class implements a Java's Collection *)
 
+val implements_collections : Tenv.t -> string -> bool
+(** Check whether class implements a Java's Collections *)
+
 val implements_pseudo_collection : Tenv.t -> string -> bool
 (** Check whether class implements a pseudo Collection with support
    for get() and size() methods *)
diff --git a/infer/src/bufferoverrun/bufferOverrunModels.ml b/infer/src/bufferoverrun/bufferOverrunModels.ml
index f7de755cd..c4848afb1 100644
--- a/infer/src/bufferoverrun/bufferOverrunModels.ml
+++ b/infer/src/bufferoverrun/bufferOverrunModels.ml
@@ -664,6 +664,15 @@ module Collection = struct
 
   let add coll_id = {exec= change_size_by ~size_f:Itv.incr coll_id; check= no_check}
 
+  let singleton_collection el_var =
+    let exec env ~ret:((id, _) as ret) mem =
+      let {exec= new_exec; check= _} = new_collection el_var in
+      let mem = new_exec env ~ret mem in
+      change_size_by ~size_f:Itv.incr id ~ret env mem
+    in
+    {exec; check= no_check}
+
+
   (** increase the size by [0, 1] because put replaces the value
      rather than add a new one when the key is found in the map *)
   let put coll_id =
@@ -877,6 +886,16 @@ module Call = struct
       ; -"std" &:: "basic_string" &::.*--> no_model
       ; +PatternMatch.implements_collection
         &:: "<init>" <>$ capt_var_exn $+ capt_exp $--> Collection.init
+        (* model sets as lists *)
+      ; +PatternMatch.implements_collections
+        &:: "singleton" <>$ capt_exp $--> Collection.singleton_collection
+      ; +PatternMatch.implements_collections
+        &:: "emptySet" <>$ capt_exp $--> Collection.new_collection
+        (* model maps as lists *)
+      ; +PatternMatch.implements_collections
+        &:: "singletonMap" <>$ capt_exp $--> Collection.singleton_collection
+      ; +PatternMatch.implements_collections
+        &:: "singletonList" <>$ capt_exp $--> Collection.singleton_collection
       ; +PatternMatch.implements_collection
         &:: "get" <>$ capt_var_exn $+ capt_exp $--> Collection.get_or_set_at_index
       ; +PatternMatch.implements_collection
diff --git a/infer/src/checkers/costModels.ml b/infer/src/checkers/costModels.ml
index 1bfdf5d81..f121239dd 100644
--- a/infer/src/checkers/costModels.ml
+++ b/infer/src/checkers/costModels.ml
@@ -34,9 +34,14 @@ module Collections = struct
     n_log_n length
 
 
-  let linear coll_exp {location} ~ret:_ inferbo_mem =
-    eval_collection_length coll_exp location ~of_function:"List.contains" inferbo_mem
-    |> BasicCost.of_non_negative_bound
+  let of_length_bound ~degree_kind coll_exp ~of_function {location} ~ret:_ inferbo_mem =
+    eval_collection_length coll_exp location inferbo_mem ~of_function
+    |> BasicCost.of_non_negative_bound ~degree_kind
+
+
+  let linear = of_length_bound ~degree_kind:Polynomials.DegreeKind.Linear
+
+  let logarithmic = of_length_bound ~degree_kind:Polynomials.DegreeKind.Log
 end
 
 let provider_get {pname; location} ~ret:(_, ret_typ) _ : BasicCost.t =
@@ -83,8 +88,24 @@ module Call = struct
   let dispatch : (Tenv.t, model) ProcnameDispatcher.Call.dispatcher =
     let open ProcnameDispatcher.Call in
     make_dispatcher
-      [ -"java.util.Collections" &:: "sort" $ capt_exp $--> Collections.sort
-      ; +PatternMatch.implements_list &:: "contains" <>$ capt_exp $+...$--> Collections.linear
+      [ +PatternMatch.implements_collections &:: "sort" $ capt_exp $--> Collections.sort
+      ; +PatternMatch.implements_list &:: "contains" <>$ capt_exp
+        $+...$--> Collections.linear ~of_function:"List.contains"
+      ; +PatternMatch.implements_collections
+        &:: "binarySearch" <>$ capt_exp
+        $+...$--> Collections.logarithmic ~of_function:"Collections.binarySearch"
+      ; +PatternMatch.implements_collections
+        &:: "copy" <>$ capt_exp
+        $+...$--> Collections.linear ~of_function:"Collections.copy"
+      ; +PatternMatch.implements_collections
+        &:: "fill" <>$ capt_exp
+        $+...$--> Collections.linear ~of_function:"Collections.fill"
+      ; +PatternMatch.implements_collections
+        &:: "reverse" <>$ capt_exp
+        $+...$--> Collections.linear ~of_function:"Collections.reverse"
+      ; +PatternMatch.implements_collections
+        &:: "shuffle" <>$ capt_exp
+        $+...$--> Collections.linear ~of_function:"Collections.shuffle"
       ; +PatternMatch.implements_lang "String"
         &:: "substring" <>$ capt_exp $+ capt_exp $--> String.substring
       ; +PatternMatch.implements_lang "String"
diff --git a/infer/tests/codetoanalyze/java/performance/ArrayListTest.java b/infer/tests/codetoanalyze/java/performance/ArrayListTest.java
index ffb9ca0e9..c4cd6026d 100644
--- a/infer/tests/codetoanalyze/java/performance/ArrayListTest.java
+++ b/infer/tests/codetoanalyze/java/performance/ArrayListTest.java
@@ -251,4 +251,5 @@ public class ArrayListTest {
     // l.length
     for (int i = 0; i < slist.size(); i++) {}
   }
+
 }
diff --git a/infer/tests/codetoanalyze/java/performance/CollectionsTest.java b/infer/tests/codetoanalyze/java/performance/CollectionsTest.java
new file mode 100644
index 000000000..83ab21069
--- /dev/null
+++ b/infer/tests/codetoanalyze/java/performance/CollectionsTest.java
@@ -0,0 +1,49 @@
+/*
+ * Copyright (c) 2019-present, Facebook, Inc.
+ *
+ * This source code is licensed under the MIT license found in the
+ * LICENSE file in the root directory of this source tree.
+ */
+import java.util.Collections;
+import java.util.List;
+import java.util.Random;
+import java.util.Set;
+
+class CollectionsTest {
+
+  int binary_search_log(List<String> list) {
+    return Collections.binarySearch(list, "x");
+  }
+
+  void shuffle_linear(List<String> list, Random mRandom) {
+    Collections.shuffle(list, mRandom);
+    for (int i = 0; i < list.size(); i++) {}
+  }
+
+  void singletonSet_constant() {
+    Set<String> set = Collections.singleton("ezgi");
+    for (String s : set) {}
+  }
+
+  void singletonList_constant(String el) {
+    List<String> list = Collections.singletonList(el);
+    for (String s : list) {}
+  }
+
+  void fill_linear(List<String> list, String el) {
+    Collections.fill(list, el);
+  }
+
+  void reverse_linear(List<String> list) {
+    Collections.reverse(list);
+  }
+
+  void reverse_constant(String el) {
+    List<String> list = Collections.singletonList(el);
+    Collections.reverse(list);
+  }
+
+  void copy_linear(List<String> list_from, List<String> list_to) {
+    Collections.copy(list_to, list_from);
+  }
+}
diff --git a/infer/tests/codetoanalyze/java/performance/issues.exp b/infer/tests/codetoanalyze/java/performance/issues.exp
index f82b3f3f9..253868279 100644
--- a/infer/tests/codetoanalyze/java/performance/issues.exp
+++ b/infer/tests/codetoanalyze/java/performance/issues.exp
@@ -51,6 +51,13 @@ codetoanalyze/java/performance/CollectionTest.java, CollectionTest.iterate_over_
 codetoanalyze/java/performance/CollectionTest.java, CollectionTest.loop_over_call(int,CollectionTest$MyCollection):void, 1, EXPENSIVE_EXECUTION_CALL, no_bucket, ERROR, [with estimated cost 2 + 15 ⋅ size + 5 ⋅ size × list.length, degree = 2,{list.length},call to void CollectionTest.iterate_over_mycollection(CollectionTest$MyCollection),Loop at line 17,{size},Loop at line 41]
 codetoanalyze/java/performance/CollectionTest.java, CollectionTest.nested_iterator_qubic(int,CollectionTest$MyCollection,CollectionTest$MyCollection):void, 1, EXPENSIVE_EXECUTION_CALL, no_bucket, ERROR, [with estimated cost 4 + 13 ⋅ (list1.length - 1) + 28 ⋅ (list1.length - 1) × (list2.length - 1) + 5 ⋅ (list1.length - 1) × (list2.length - 1) × list1.length + 5 ⋅ (list1.length - 1) × (list2.length - 1) × list1.length + 3 ⋅ (list1.length - 1) × list2.length + 3 ⋅ list1.length, degree = 3,{list1.length},Loop at line 55,{list2.length},Loop at line 56,{list1.length},call to void CollectionTest.iterate_over_mycollection(CollectionTest$MyCollection),Loop at line 17,{list1.length},call to void CollectionTest.iterate_over_mycollection(CollectionTest$MyCollection),Loop at line 17,{list2.length - 1},Loop at line 56,{list1.length - 1},Loop at line 55]
 codetoanalyze/java/performance/CollectionTest.java, CollectionTest.sparse_array_linear(android.util.SparseArray):void, 1, EXPENSIVE_EXECUTION_CALL, no_bucket, ERROR, [with estimated cost 2 + 5 ⋅ arr.length + 3 ⋅ (arr.length + 1), degree = 1,{arr.length + 1},Loop at line 64,{arr.length},Loop at line 64]
+codetoanalyze/java/performance/CollectionsTest.java, CollectionsTest.binary_search_log(java.util.List):int, 1, EXPENSIVE_EXECUTION_CALL, no_bucket, ERROR, [with estimated cost 2 + log(list.length), degree = 0 + 1⋅log,{list.length},Modeled call to Collections.binarySearch]
+codetoanalyze/java/performance/CollectionsTest.java, CollectionsTest.copy_linear(java.util.List,java.util.List):void, 1, EXPENSIVE_EXECUTION_CALL, no_bucket, ERROR, [with estimated cost 3 + list_to.length, degree = 1,{list_to.length},Modeled call to Collections.copy]
+codetoanalyze/java/performance/CollectionsTest.java, CollectionsTest.fill_linear(java.util.List,java.lang.String):void, 1, EXPENSIVE_EXECUTION_CALL, no_bucket, ERROR, [with estimated cost 3 + list.length, degree = 1,{list.length},Modeled call to Collections.fill]
+codetoanalyze/java/performance/CollectionsTest.java, CollectionsTest.reverse_linear(java.util.List):void, 1, EXPENSIVE_EXECUTION_CALL, no_bucket, ERROR, [with estimated cost 2 + list.length, degree = 1,{list.length},Modeled call to Collections.reverse]
+codetoanalyze/java/performance/CollectionsTest.java, CollectionsTest.shuffle_linear(java.util.List,java.util.Random):void, 1, EXPENSIVE_EXECUTION_CALL, no_bucket, ERROR, [with estimated cost 3 + list.length, degree = 1,{list.length},Modeled call to Collections.shuffle]
+codetoanalyze/java/performance/CollectionsTest.java, CollectionsTest.singletonList_constant(java.lang.String):void, 2, CONDITION_ALWAYS_FALSE, no_bucket, WARNING, [Here]
+codetoanalyze/java/performance/CollectionsTest.java, CollectionsTest.singletonSet_constant():void, 2, CONDITION_ALWAYS_FALSE, no_bucket, WARNING, [Here]
 codetoanalyze/java/performance/Compound_loop.java, codetoanalyze.java.performance.Compound_loop.compound_while(int):int, 3, CONDITION_ALWAYS_TRUE, no_bucket, WARNING, [Here]
 codetoanalyze/java/performance/Compound_loop.java, codetoanalyze.java.performance.Compound_loop.compound_while(int):int, 3, EXPENSIVE_EXECUTION_CALL, no_bucket, ERROR, [with estimated cost 4 + 5 ⋅ m + 2 ⋅ (1+max(0, m)), degree = 1,{1+max(0, m)},Loop at line 15,{m},Loop at line 15]
 codetoanalyze/java/performance/Compound_loop.java, codetoanalyze.java.performance.Compound_loop.nested_while_and_or(int):int, 3, CONDITION_ALWAYS_TRUE, no_bucket, WARNING, [Here]