diff --git a/src/dataframe/insertion.jl b/src/dataframe/insertion.jl
index b790155b1..d04829499 100644
--- a/src/dataframe/insertion.jl
+++ b/src/dataframe/insertion.jl
@@ -1103,8 +1103,14 @@ end
 function Base.push!(df::DataFrame, @nospecialize rows...;
                     cols::Symbol=:setequal,
                     promote::Bool=(cols in [:union, :subset]))
+    if isempty(rows)
+        if !(cols in (:orderequal, :setequal, :intersect, :subset, :union))
+            throw(ArgumentError("`cols` keyword argument must be " *
+                                ":orderequal, :setequal, :intersect, :subset or :union)"))
+        end
+    end
     with_names_count = count(rows) do row
-        row isa Union{AbstractDict,NamedTuple,Tables.AbstractRow}
+        row isa Union{DataFrameRow,AbstractDict,NamedTuple,Tables.AbstractRow}
     end
     if 0 < with_names_count < length(rows)
         throw(ArgumentError("Mixing rows with column names and without column names " *
@@ -1116,8 +1122,14 @@ end
 function Base.pushfirst!(df::DataFrame, @nospecialize rows...;
                          cols::Symbol=:setequal,
                          promote::Bool=(cols in [:union, :subset]))
+    if isempty(rows)
+        if !(cols in (:orderequal, :setequal, :intersect, :subset, :union))
+            throw(ArgumentError("`cols` keyword argument must be " *
+                                ":orderequal, :setequal, :intersect, :subset or :union)"))
+        end
+    end
     with_names_count = count(rows) do row
-        row isa Union{AbstractDict,NamedTuple,Tables.AbstractRow}
+        row isa Union{DataFrameRow,AbstractDict,NamedTuple,Tables.AbstractRow}
     end
     if 0 < with_names_count < length(rows)
         throw(ArgumentError("Mixing rows with column names and without column names " *
diff --git a/test/insertion.jl b/test/insertion.jl
index 8c60e2349..3e9bb7d5f 100644
--- a/test/insertion.jl
+++ b/test/insertion.jl
@@ -1394,9 +1394,9 @@ end
               DataFrame(a=[3, 5, 7, 1], b=[4, 6, 8, 2])
     end
 
-    for x in (DataFrame(a=3, b=4)[1, :], (a=3, b=4), (3, 4)),
-        y in (DataFrame(a=5, b=6)[1, :], (a=5, b=6), (5, 6)),
-        z in (DataFrame(a=7, b=8)[1, :], (a=7, b=8), (7, 8))
+    for x in (DataFrame(a=3, b=4)[1, :], (a=3, b=4)),
+        y in (DataFrame(a=5, b=6)[1, :], (a=5, b=6)),
+        z in (DataFrame(a=7, b=8)[1, :], (a=7, b=8))
         @test push!(copy(df), x, y) ==
               DataFrame(a=1:2:5, b=2:2:6)
         @test push!(copy(df), x, y, z) ==
@@ -1405,7 +1405,7 @@ end
               DataFrame(a=[3, 5, 1], b=[4, 6, 2])
         @test pushfirst!(copy(df), x, y, z) ==
               DataFrame(a=[3, 5, 7, 1], b=[4, 6, 8, 2])
-        for cols in (:orderequal, :setequal)
+        for cols in (:orderequal, :setequal, :union, :subset, :intersect)
             @test push!(copy(df), x, y, cols=cols) ==
                 DataFrame(a=1:2:5, b=2:2:6)
             @test push!(copy(df), x, y, z, cols=cols) ==
@@ -1417,6 +1417,17 @@ end
         end
     end
 
+    for x in ((3, 4), [3, 4]), y in ((5, 6), [5, 6]), z in ((7, 8), [7, 8])
+        @test push!(copy(df), x, y) ==
+              DataFrame(a=1:2:5, b=2:2:6)
+        @test push!(copy(df), x, y, z) ==
+              DataFrame(a=1:2:7, b=2:2:8)
+        @test pushfirst!(copy(df), x, y) ==
+              DataFrame(a=[3, 5, 1], b=[4, 6, 2])
+        @test pushfirst!(copy(df), x, y, z) ==
+              DataFrame(a=[3, 5, 7, 1], b=[4, 6, 8, 2])
+    end
+
     for x in (DataFrame(a=3, b=4), (a=[3], b=[4]), [(a=3, b=4)]),
         y in (DataFrame(a=5, c=6), (a=[5], c=[6]), [(a=5, c=6)]),
         z in (DataFrame(a="7", d=8), (a=["7"], d=[8]), [(a="7", d=8)])
@@ -1457,9 +1468,9 @@ end
     @test_throws ArgumentError push!(df, (1, 2), (1, 2), cols=:union)
     @test_throws ArgumentError pushfirst!(df, (1, 2), (1, 2), cols=:union)
 
-    @test insert!(DataFrame(a=1:3, b=11:13), 2, (0, 10), cols=:orderequal) ==
+    @test insert!(DataFrame(a=1:3, b=11:13), 2, (0, 10), cols=:setequal) ==
           DataFrame(a=[1, 0, 2, 3], b=[11, 10, 12, 13])
-    @test_throws ArgumentError insert!(df, 1, (1, 2), cols=:union)
+    @test_throws ArgumentError insert!(df, 1, (1, 2), cols=:orderequal)
 end
 
 end # module