diff --git a/Project.toml b/Project.toml
index f377285a4..f5eca4884 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "Compat"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
-version = "3.31.0"
+version = "3.31.1"
 
 [deps]
 Base64 = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
diff --git a/README.md b/README.md
index 1512d5f5c..62f23b5d2 100644
--- a/README.md
+++ b/README.md
@@ -54,6 +54,10 @@ changes in `julia`.
 
 ## Supported features
 
+* Two argument methods `findmax(f, domain)`, `argmax(f, domain)` and the corresponding `min` versions ([#35316], [#41076]) (since Compat 3.31.1)
+
+* `isunordered(x)` returns true if `x` is value that is normally unordered, such as `NaN` or `missing` ([#35316]) (since Compat 3.31.1)
+
 * `get` accepts tuples and numbers ([#41007], [#41032]) (since Compat 3.31)
 
 * `muladd(A,B,z)` now accepts arrays ([#37065]) (since Compat 3.30)
@@ -252,3 +256,5 @@ Note that you should specify the correct minimum version for `Compat` in the
 [#37065]: https://github.com/JuliaLang/julia/pull/37065
 [#41007]: https://github.com/JuliaLang/julia/pull/41007
 [#41032]: https://github.com/JuliaLang/julia/pull/41032
+[#35316]: https://github.com/JuliaLang/julia/pull/35316
+[#41076]: https://github.com/JuliaLang/julia/pull/41076
diff --git a/src/Compat.jl b/src/Compat.jl
index 95f978845..b5726826a 100644
--- a/src/Compat.jl
+++ b/src/Compat.jl
@@ -957,21 +957,23 @@ if VERSION < v"1.2.0-DEV.246"
 end
 
 if VERSION < v"1.7.0-DEV.119"
-    # Part of https://github.com/JuliaLang/julia/pull/35316
+    # Part of:
+    # https://github.com/JuliaLang/julia/pull/35316
+    # https://github.com/JuliaLang/julia/pull/41076
     isunordered(x) = false
     isunordered(x::AbstractFloat) = isnan(x)
     isunordered(x::Missing) = true
 
     isgreater(x, y) = isunordered(x) || isunordered(y) ? isless(x, y) : isless(y, x)
 
-    Base.findmax(f, domain) = mapfoldl(x -> (f(x), x), _rf_findmax, domain)
-    _rf_findmax((fm, m), (fx, x)) = isless(fm, fx) ? (fx, x) : (fm, m)
+    Base.findmax(f, domain) = mapfoldl( ((k, v),) -> (f(v), k), _rf_findmax, pairs(domain) )
+    _rf_findmax((fm, im), (fx, ix)) = isless(fm, fx) ? (fx, ix) : (fm, im)
 
-    Base.findmin(f, domain) = mapfoldl(x -> (f(x), x), _rf_findmin, domain)
-    _rf_findmin((fm, m), (fx, x)) = isgreater(fm, fx) ? (fx, x) : (fm, m)
+    Base.findmin(f, domain) = mapfoldl( ((k, v),) -> (f(v), k), _rf_findmin, pairs(domain) )
+    _rf_findmin((fm, im), (fx, ix)) = isgreater(fm, fx) ? (fx, ix) : (fm, im)
 
-    Base.argmax(f, domain) = findmax(f, domain)[2]
-    Base.argmin(f, domain) = findmin(f, domain)[2]
+    Base.argmax(f, domain) = mapfoldl(x -> (f(x), x), _rf_findmax, domain)[2]
+    Base.argmin(f, domain) = mapfoldl(x -> (f(x), x), _rf_findmin, domain)[2]
 end
 
 # Part of: https://github.com/JuliaLang/julia/pull/36018
diff --git a/test/runtests.jl b/test/runtests.jl
index 13fe0926f..8738401e2 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -946,25 +946,26 @@ end
 end
 
 # https://github.com/JuliaLang/julia/pull/35316
+# https://github.com/JuliaLang/julia/pull/41076
 @testset "2arg" begin
     @testset "findmin(f, domain)" begin
         @test findmin(-, 1:10) == (-10, 10)
-        @test findmin(identity, [1, 2, 3, missing]) === (missing, missing)
-        @test findmin(identity, [1, NaN, 3, missing]) === (missing, missing)
-        @test findmin(identity, [1, missing, NaN, 3]) === (missing, missing)
-        @test findmin(identity, [1, NaN, 3]) === (NaN, NaN)
-        @test findmin(identity, [1, 3, NaN]) === (NaN, NaN)
-        @test all(findmin(cos, 0:π/2:2π) .≈ (-1.0, π))
+        @test findmin(identity, [1, 2, 3, missing]) === (missing, 4)
+        @test findmin(identity, [1, NaN, 3, missing]) === (missing, 4)
+        @test findmin(identity, [1, missing, NaN, 3]) === (missing, 2)
+        @test findmin(identity, [1, NaN, 3]) === (NaN, 2)
+        @test findmin(identity, [1, 3, NaN]) === (NaN, 3)
+        @test all(findmin(cos, 0:π/2:2π) .≈ (-1.0, 3))
     end
 
     @testset "findmax(f, domain)" begin
         @test findmax(-, 1:10) == (-1, 1)
-        @test findmax(identity, [1, 2, 3, missing]) === (missing, missing)
-        @test findmax(identity, [1, NaN, 3, missing]) === (missing, missing)
-        @test findmax(identity, [1, missing, NaN, 3]) === (missing, missing)
-        @test findmax(identity, [1, NaN, 3]) === (NaN, NaN)
-        @test findmax(identity, [1, 3, NaN]) === (NaN, NaN)
-        @test findmax(cos, 0:π/2:2π) == (1.0, 0.0)
+        @test findmax(identity, [1, 2, 3, missing]) === (missing, 4)
+        @test findmax(identity, [1, NaN, 3, missing]) === (missing, 4)
+        @test findmax(identity, [1, missing, NaN, 3]) === (missing, 2)
+        @test findmax(identity, [1, NaN, 3]) === (NaN, 2)
+        @test findmax(identity, [1, 3, NaN]) === (NaN, 3)
+        @test findmax(cos, 0:π/2:2π) == (1.0, 1)
     end
 
     @testset "argmin(f, domain)" begin