diff --git a/base/math.jl b/base/math.jl
index 6ed69188371dd..4626a684d5f0e 100644
--- a/base/math.jl
+++ b/base/math.jl
@@ -95,11 +95,10 @@ julia> clamp.([11, 8, 5], 10, 6)  # an example where lo > hi
  10
 ```
 """
-clamp(x::X, lo::L, hi::H) where {X,L,H} =
-    ifelse(x > hi, convert(promote_type(X,L,H), hi),
-           ifelse(x < lo,
-                  convert(promote_type(X,L,H), lo),
-                  convert(promote_type(X,L,H), x)))
+function clamp(x::X, lo::L, hi::H) where {X,L,H}
+    T = promote_type(X, L, H)
+    return (x > hi) ? convert(T, hi) : (x < lo) ? convert(T, lo) : convert(T, x)
+end
 
 """
     clamp(x, T)::T
@@ -120,7 +119,14 @@ julia> trunc(Int, 4pi^2)
 39
 ```
 """
-clamp(x, ::Type{T}) where {T<:Integer} = clamp(x, typemin(T), typemax(T)) % T
+function clamp(x, ::Type{T}) where {T<:Integer}
+    # delegating to clamp(x, typemin(T), typemax(T)) would promote types
+    # this way, we avoid unnecessary conversions
+    # think of, e.g., clamp(big(2) ^ 200, Int16)
+    lo = typemin(T)
+    hi = typemax(T)
+    return (x > hi) ? hi : (x < lo) ? lo : convert(T, x)
+end
 
 
 """
diff --git a/test/math.jl b/test/math.jl
index f3c6dc5bb103f..c88905018fb3a 100644
--- a/test/math.jl
+++ b/test/math.jl
@@ -47,6 +47,17 @@ has_fma = Dict(
         clamp!(x, 1, 3)
         @test x == [1.0, 1.0, 2.0, 3.0, 3.0]
     end
+
+    @test clamp(typemax(UInt64), Int64) === typemax(Int64)
+    @test clamp(typemin(Int), UInt64) === typemin(UInt64)
+    @test clamp(Int16(-1), UInt16) === UInt16(0)
+    @test clamp(-1, 2, UInt(0)) === UInt(2)
+    @test clamp(typemax(UInt16), Int16) === Int16(32767)
+
+    # clamp should not allocate a BigInt for typemax(Int16)
+    x = big(2) ^ 100
+    @test (@allocated clamp(x, Int16)) == 0
+
 end
 
 @testset "constants" begin