diff --git a/base/compiler/abstractinterpretation.jl b/base/compiler/abstractinterpretation.jl
index 329988744fe23..a5d3395bca486 100644
--- a/base/compiler/abstractinterpretation.jl
+++ b/base/compiler/abstractinterpretation.jl
@@ -715,7 +715,7 @@ function concrete_eval_eligible(interp::AbstractInterpreter,
     isoverlayed(method_table(interp)) && result.edge_effects.overlayed && return false
     return f !== nothing &&
            result.edge !== nothing &&
-           is_total_or_error(result.edge_effects) &&
+           is_concrete_eval_eligible(result.edge_effects) &&
            is_all_const_arg(arginfo)
 end
 
diff --git a/base/compiler/types.jl b/base/compiler/types.jl
index 0d8275ac0e7a0..b66c6213a0221 100644
--- a/base/compiler/types.jl
+++ b/base/compiler/types.jl
@@ -78,13 +78,13 @@ function Effects(e::Effects = EFFECTS_UNKNOWN;
         inbounds_taints_consistency)
 end
 
-is_total_or_error(effects::Effects) =
+is_concrete_eval_eligible(effects::Effects) =
     effects.consistent === ALWAYS_TRUE &&
     effects.effect_free === ALWAYS_TRUE &&
     effects.terminates === ALWAYS_TRUE
 
 is_total(effects::Effects) =
-    is_total_or_error(effects) &&
+    is_concrete_eval_eligible(effects) &&
     effects.nothrow === ALWAYS_TRUE
 
 is_removable_if_unused(effects::Effects) =
diff --git a/base/expr.jl b/base/expr.jl
index de1045d6addfe..de8264a14e1b6 100644
--- a/base/expr.jl
+++ b/base/expr.jl
@@ -512,11 +512,24 @@ This `setting` combines the following other assertions:
 - `:terminates_globally`
 and is a convenient shortcut.
 
+---
+# `:total_but_may_throw`
+
+This `setting` combines the following other assertions:
+- `:consistent`
+- `:effect_free`
+- `:terminates_globally`
+and is a convenient shortcut.
+
 !!! note
-    `@assume_effects :total` is similar to `@Base.pure` with the primary
+    This setting is particularly useful since it allows the compiler to evaluate a call of
+    the applied method when all the call arguments are fully known, no matter if the call
+    results in an error or not.
+
+    `@assume_effects :total_but_may_throw` is similar to `Base.@pure` with the primary
     distinction that the `:consistent`-cy requirement applies world-age wise rather
     than globally as described above. However, in particular, a method annotated
-    `@Base.pure` is always `:total`.
+    `Base.@pure` should always be `:total` or `:total_but_may_throw`.
 """
 macro assume_effects(args...)
     (consistent, effect_free, nothrow, terminates_globally, terminates_locally) =
@@ -537,12 +550,14 @@ macro assume_effects(args...)
             terminates_locally = true
         elseif setting === :total
             consistent = effect_free = nothrow = terminates_globally = true
+        elseif setting === :total_but_may_throw
+            consistent = effect_free = terminates_globally = true
         else
             throw(ArgumentError("@assume_effects $setting not supported"))
         end
     end
     ex = args[end]
-    isa(ex, Expr) || throw(ArgumentError("Bad expression `$ex` in @constprop [settings] ex"))
+    isa(ex, Expr) || throw(ArgumentError("Bad expression `$ex` in `@assume_effects [settings] ex`"))
     if ex.head === :macrocall && ex.args[1] == Symbol("@ccall")
         ex.args[1] = GlobalRef(Base, Symbol("@ccall_effects"))
         insert!(ex.args, 3, Core.Compiler.encode_effects_override(Core.Compiler.EffectsOverride(
diff --git a/test/compiler/inline.jl b/test/compiler/inline.jl
index cc94ace0026df..4743e036faf0a 100644
--- a/test/compiler/inline.jl
+++ b/test/compiler/inline.jl
@@ -1088,11 +1088,11 @@ recur_termination22(x) = x * recur_termination21(x-1)
     recur_termination21(12) + recur_termination22(12)
 end
 
-const ___CONST_DICT___ = Dict{Any,Any}(:a => 1, :b => 2)
-Base.@assume_effects :consistent :effect_free :terminates_globally consteval(
+const ___CONST_DICT___ = Dict{Any,Any}(Symbol(c) => i for (i, c) in enumerate('a':'z'))
+Base.@assume_effects :total_but_may_throw concrete_eval(
     f, args...; kwargs...) = f(args...; kwargs...)
 @test fully_eliminated() do
-    consteval(getindex, ___CONST_DICT___, :a)
+    concrete_eval(getindex, ___CONST_DICT___, :a)
 end
 
 # https://github.com/JuliaLang/julia/issues/44732