diff --git a/base/twiceprecision.jl b/base/twiceprecision.jl
index 80d1917ea599f..23cc2690f5b44 100644
--- a/base/twiceprecision.jl
+++ b/base/twiceprecision.jl
@@ -122,8 +122,6 @@ end
 
 function colon{T<:Union{Float16,Float32,Float64}}(start::T, step::T, stop::T)
     step == 0 && throw(ArgumentError("range step cannot be zero"))
-    len = max(0, floor(Int, (stop-start)/step) + 1)
-    # Because len might be too small by 1 due to roundoff error, let's
     # see if the inputs have exact rational approximations (and if so,
     # perform all computations in terms of the rationals)
     step_n, step_d = rat(step)
@@ -149,6 +147,9 @@ function colon{T<:Union{Float16,Float32,Float64}}(start::T, step::T, stop::T)
         end
     end
     # Fallback, taking start and step literally
+    len = max(0, floor(Int, (stop-start)/step) + 1)
+    stop′ = start + len*step
+    len += (start < stop′ <= stop) + (start > stop′ >= stop)
     StepRangeLen(TwicePrecision(start, zero(T)), twiceprecision(step, nbitslen(T, len, 1)), len)
 end
 
diff --git a/test/ranges.jl b/test/ranges.jl
index ca94a1e00b7af..7c8c6c3e56b38 100644
--- a/test/ranges.jl
+++ b/test/ranges.jl
@@ -333,6 +333,29 @@ for T = (Float32, Float64,),# BigFloat),
     @test [r[n:-2:1];] == [r;][n:-2:1]
 end
 
+# issue #20373 (unliftable ranges with exact end points)
+@test [3*0.05:0.05:0.2;]    == [linspace(3*0.05,0.2,2);]   == [3*0.05,0.2]
+@test [0.2:-0.05:3*0.05;]   == [linspace(0.2,3*0.05,2);]   == [0.2,3*0.05]
+@test [-3*0.05:-0.05:-0.2;] == [linspace(-3*0.05,-0.2,2);] == [-3*0.05,-0.2]
+@test [-0.2:0.05:-3*0.05;]  == [linspace(-0.2,-3*0.05,2);] == [-0.2,-3*0.05]
+
+for T = (Float32, Float64,), i = 1:2^15, n = 1:5
+    start, step = randn(T), randn(T)
+    stop = start + (n-1)*step
+    r = start:step:stop
+    @test n == length(r)
+    # FIXME: these fail some small portion of the time
+    @test_skip start == first(r)
+    @test_skip stop  == last(r)
+    # FIXME: linspace construction fails on 32-bit
+    Sys.WORD_SIZE == 64 || continue
+    l = linspace(start,stop,n)
+    @test n == length(l)
+    # FIXME: these fail some small portion of the time
+    @test_skip start == first(l)
+    @test_skip stop  == last(l)
+end
+
 # linspace & ranges with very small endpoints
 for T = (Float32, Float64)
     z = zero(T)