diff --git a/loopy/check.py b/loopy/check.py
index 0d2bbff7cf8d6f9e63a33dc2c8814f29afae70f0..da49c1d116df1a9fbf92e8ef41822b6741405604 100644
--- a/loopy/check.py
+++ b/loopy/check.py
@@ -184,6 +184,19 @@ def check_for_inactive_iname_access(kernel):
                         ", ".join(expression_inames - kernel.insn_inames(insn))))
 
 
+def check_for_unused_inames(kernel):
+    # Warn if kernel has unused inames
+    from loopy.transform.iname import get_used_inames
+    unused_inames = kernel.all_inames() - get_used_inames(kernel)
+    if unused_inames:
+        warn_with_kernel(
+            kernel, "unused_inames",
+            "Found unused inames in kernel: %s "
+            "Unused inames during linearization will be prohibited in "
+            "Loopy version 2021.X."
+            % unused_inames)
+
+
 def _is_racing_iname_tag(tv, tag):
     from loopy.kernel.data import (AddressSpace,
             LocalIndexTagBase, GroupIndexTag, ConcurrentTag, auto)
@@ -658,6 +671,7 @@ def pre_schedule_checks(kernel):
         check_loop_priority_inames_known(kernel)
         check_multiple_tags_allowed(kernel)
         check_for_inactive_iname_access(kernel)
+        check_for_unused_inames(kernel)
         check_for_write_races(kernel)
         check_for_data_dependent_parallel_bounds(kernel)
         check_bounds(kernel)
diff --git a/loopy/preprocess.py b/loopy/preprocess.py
index 23c4b7fbd9e55006dd17ed9b127e598a14ee17a2..221233ed010e4cd3c574cf047f73263063152d93 100644
--- a/loopy/preprocess.py
+++ b/loopy/preprocess.py
@@ -37,6 +37,7 @@ from loopy.version import DATA_MODEL_VERSION
 from loopy.kernel.data import make_assignment, filter_iname_tags_by_type
 # for the benefit of loopy.statistics, for now
 from loopy.type_inference import infer_unknown_types
+from loopy.transform.iname import remove_any_newly_unused_inames
 
 import logging
 logger = logging.getLogger(__name__)
@@ -882,6 +883,7 @@ def _insert_subdomain_into_domain_tree(kernel, domains, subdomain):
 # }}}
 
 
+@remove_any_newly_unused_inames
 def realize_reduction(kernel, insn_id_filter=None, unknown_types_ok=True,
                       automagic_scans_ok=False, force_scan=False,
                       force_outer_iname_for_scan=None):
@@ -1924,8 +1926,6 @@ def realize_reduction(kernel, insn_id_filter=None, unknown_types_ok=True,
 
     kernel = lp.tag_inames(kernel, new_iname_tags)
 
-    # TODO: remove unused inames...
-
     kernel = (
             _hackily_ensure_multi_assignment_return_values_are_scoped_private(
                 kernel))
diff --git a/loopy/transform/iname.py b/loopy/transform/iname.py
index 96c8252ef7e6622250e9006b2275ef7816700b5c..ae717e1c7550b697c23b9d032fd795c362e387f0 100644
--- a/loopy/transform/iname.py
+++ b/loopy/transform/iname.py
@@ -1184,6 +1184,19 @@ def rename_iname(knl, old_iname, new_iname, existing_ok=False, within=None):
 
 # {{{ remove unused inames
 
+def get_used_inames(knl):
+    import loopy as lp
+    exp_knl = lp.expand_subst(knl)
+
+    used_inames = set()
+    for insn in exp_knl.instructions:
+        used_inames.update(
+                exp_knl.insn_inames(insn.id)
+                | insn.reduction_inames())
+
+    return used_inames
+
+
 def remove_unused_inames(knl, inames=None):
     """Delete those among *inames* that are unused, i.e. project them
     out of the domain. If these inames pose implicit restrictions on
@@ -1204,17 +1217,7 @@ def remove_unused_inames(knl, inames=None):
 
     # {{{ check which inames are unused
 
-    import loopy as lp
-    exp_knl = lp.expand_subst(knl)
-
-    inames = set(inames)
-    used_inames = set()
-    for insn in exp_knl.instructions:
-        used_inames.update(
-                exp_knl.insn_inames(insn.id)
-                | insn.reduction_inames())
-
-    unused_inames = inames - used_inames
+    unused_inames = set(inames) - get_used_inames(knl)
 
     # }}}
 
@@ -1235,6 +1238,33 @@ def remove_unused_inames(knl, inames=None):
 
     return knl
 
+
+def remove_any_newly_unused_inames(transformation_func):
+    from functools import wraps
+
+    @wraps(transformation_func)
+    def wrapper(knl, *args, **kwargs):
+
+        # check for remove_unused_inames argument, default: True
+        remove_newly_unused_inames = kwargs.pop("remove_newly_unused_inames", True)
+
+        if remove_newly_unused_inames:
+            # determine which inames were already unused
+            inames_already_unused = knl.all_inames() - get_used_inames(knl)
+
+            # call transform
+            transformed_knl = transformation_func(knl, *args, **kwargs)
+
+            # Remove inames that are unused due to transform
+            return remove_unused_inames(
+                transformed_knl,
+                transformed_knl.all_inames()-inames_already_unused)
+        else:
+            # call transform
+            return transformation_func(knl, *args, **kwargs)
+
+    return wrapper
+
 # }}}
 
 
diff --git a/loopy/transform/subst.py b/loopy/transform/subst.py
index fa145fbbf3e51670f7ac42307e4ffde75df07618..717a051930e938457dae0ee4441325b3e631d2d9 100644
--- a/loopy/transform/subst.py
+++ b/loopy/transform/subst.py
@@ -27,6 +27,7 @@ import six
 from loopy.symbolic import (
         RuleAwareIdentityMapper, SubstitutionRuleMappingContext)
 from loopy.diagnostic import LoopyError
+from loopy.transform.iname import remove_any_newly_unused_inames
 
 from pytools import ImmutableRecord
 from pymbolic import var
@@ -278,6 +279,7 @@ class AssignmentToSubstChanger(RuleAwareIdentityMapper):
             return var(subst_name)(*index)
 
 
+@remove_any_newly_unused_inames
 def assignment_to_subst(kernel, lhs_name, extra_arguments=(), within=None,
         force_retain_argument=False):
     """Extract an assignment (to a temporary variable or an argument)
diff --git a/test/test_apps.py b/test/test_apps.py
index e07262dbdda8ad3c24522f7d0eb4dba8422bf0ce..71029cc9ce408f8e7fa95eaf3b766864c4beee5b 100644
--- a/test/test_apps.py
+++ b/test/test_apps.py
@@ -566,7 +566,7 @@ def test_poisson_fem(ctx_factory):
     sdim = 3
 
     knl = lp.make_kernel(
-            "{ [c,i,j,k,ell,ell2,ell3]: \
+            "{ [c,i,j,k,ell,ell2]: \
             0 <= c < nels and \
             0 <= i < nbf and \
             0 <= j < nbf and \
diff --git a/test/test_domain.py b/test/test_domain.py
index ebfde850907d68bebf06076fbf1c87d8bb093f71..5daf84eaa5b7ffd1647daf4b35acd7a5de91c5d1 100644
--- a/test/test_domain.py
+++ b/test/test_domain.py
@@ -111,7 +111,7 @@ def test_eq_constraint(ctx_factory):
     ctx = ctx_factory()
 
     knl = lp.make_kernel(
-            "{[i,j]: 0<= i,j < 32}",
+            "{[i]: 0<= i < 32}",
             [
                 "a[i] = b[i]"
                 ],
diff --git a/test/test_loopy.py b/test/test_loopy.py
index 6b78ac26b78d8c85dab3cd41af0ce1d99d52ec07..61a3f167be66f1c99adc3a52473d8edc747479e1 100644
--- a/test/test_loopy.py
+++ b/test/test_loopy.py
@@ -177,7 +177,7 @@ def test_simple_side_effect(ctx_factory):
     ctx = ctx_factory()
 
     knl = lp.make_kernel(
-            "{[i,j]: 0<=i,j<100}",
+            "{[i]: 0<=i<100}",
             """
                 a[i] = a[i] + 1
                 """,
@@ -456,7 +456,7 @@ def test_nonlinear_index(ctx_factory):
     ctx = ctx_factory()
 
     knl = lp.make_kernel(
-            "{[i,j]: 0<=i,j<n }",
+            "{[i]: 0<=i<n }",
             """
                 a[i*i] = 17
                 """,
@@ -564,7 +564,7 @@ def test_dependent_domain_insn_iname_finding(ctx_factory):
 
     knl = lp.make_kernel([
             "{[isrc_box]: 0<=isrc_box<nsrc_boxes}",
-            "{[isrc,idim]: isrc_start<=isrc<isrc_end and 0<=idim<dim}",
+            "{[isrc]: isrc_start<=isrc<isrc_end}",
             ],
             """
                 <> src_ibox = source_boxes[isrc_box]
@@ -769,7 +769,7 @@ def test_multiple_writes_to_local_temporary():
     # writes are OK.
 
     knl = lp.make_kernel(
-        "{[i,e]: 0<=i<5 and 0<=e<nelements}",
+        "{[i]: 0<=i<5}",
         """
         <> temp[i, 0] = 17
         temp[i, 1] = 15
@@ -952,7 +952,7 @@ def test_atomic_init(dtype):
     vec_width = 4
 
     knl = lp.make_kernel(
-            "{ [i,j]: 0<=i<100 }",
+            "{ [i]: 0<=i<100 }",
             """
             out[i%4] = 0 {id=init, atomic=init}
             """,
@@ -1555,7 +1555,7 @@ def test_finite_difference_expr_subst(ctx_factory):
             gpu_knl, "f_subst", "inew_inner", fetch_bounding_box=True,
             default_tag="l.auto")
 
-    precomp_knl = lp.tag_inames(precomp_knl, {"j_0_outer": "unr"})
+    precomp_knl = lp.tag_inames(precomp_knl, {"j_outer": "unr"})
     precomp_knl = lp.set_options(precomp_knl, return_dict=True)
     evt, _ = precomp_knl(queue, u=u, h=h)
 
@@ -1926,8 +1926,9 @@ def test_scalars_with_base_storage(ctx_factory):
     ctx = ctx_factory()
     queue = cl.CommandQueue(ctx)
 
+    import islpy as isl
     knl = lp.make_kernel(
-            "{ [i]: 0<=i<1}",
+            [isl.BasicSet("[] -> {[]: }")],  # empty (domain w/unused inames errors)
             "a = 1",
             [lp.TemporaryVariable("a", dtype=np.float64,
                                   shape=(), base_storage="base")])
diff --git a/test/test_sem_reagan.py b/test/test_sem_reagan.py
index e022e92f3712d984c1ad68061d0052240ff9d20c..54c64e0a4d4a23b429eb83be6c0a19f482a1b922 100644
--- a/test/test_sem_reagan.py
+++ b/test/test_sem_reagan.py
@@ -48,7 +48,7 @@ def test_tim2d(ctx_factory):
 
     # K - run-time symbolic
     knl = lp.make_kernel(
-            "{[i,j,e,m,o,o2,gi]: 0<=i,j,m,o,o2<n and 0<=e<K and 0<=gi<3}",
+            "{[i,j,e,m,o,o2]: 0<=i,j,m,o,o2<n and 0<=e<K}",
             [
                 "ur(a,b) := simul_reduce(sum, o, D[a,o]*u[e,o,b])",
                 "us(a,b) := simul_reduce(sum, o2, D[b,o2]*u[e,a,o2])",
@@ -74,8 +74,8 @@ def test_tim2d(ctx_factory):
             name="semlap2D", assumptions="K>=1")
 
     knl = lp.fix_parameters(knl, n=n)
-    knl = lp.duplicate_inames(knl, "o", within="id:ur")
-    knl = lp.duplicate_inames(knl, "o", within="id:us")
+    # knl = lp.duplicate_inames(knl, "o", within="id:ur")
+    # knl = lp.duplicate_inames(knl, "o", within="id:us")
 
     seq_knl = knl
 
@@ -87,6 +87,7 @@ def test_tim2d(ctx_factory):
 
         knl = lp.precompute(knl, "ur(m,j)", ["m", "j"], default_tag="l.auto")
         knl = lp.precompute(knl, "us(i,m)", ["i", "m"], default_tag="l.auto")
+        # TODO this adds `a` and `b` to domains, which leads to unused inames
 
         knl = lp.precompute(knl, "Gux(m,j)", ["m", "j"], default_tag="l.auto")
         knl = lp.precompute(knl, "Guy(i,m)", ["i", "m"], default_tag="l.auto")
diff --git a/test/test_target.py b/test/test_target.py
index bcf85a340a29afc8772686d23c5fe3e8a03ccffd..038b2e6c06116049441fad36d033c5a6831b4dbe 100644
--- a/test/test_target.py
+++ b/test/test_target.py
@@ -231,8 +231,9 @@ def test_tuple(ctx_factory):
     ctx = ctx_factory()
     queue = cl.CommandQueue(ctx)
 
+    import islpy as isl
     knl = lp.make_kernel(
-            "{ [i]: 0 = i }",
+            [isl.BasicSet("[] -> {[]: }")],
             """
             a, b = make_tuple(1, 2.)
             """)
diff --git a/test/test_transform.py b/test/test_transform.py
index d21d2c9da7ac28f119d3c5b475116dcc4b19e871..ffef893b05fbca5a0d244ff17f379e1bb5cf27a1 100644
--- a/test/test_transform.py
+++ b/test/test_transform.py
@@ -74,7 +74,7 @@ def test_collect_common_factors(ctx_factory):
     ctx = ctx_factory()
 
     knl = lp.make_kernel(
-            "{[i,j,k]: 0<=i,j<n}",
+            "{[i,j]: 0<=i,j<n}",
             """
             <float32> out_tmp = 0 {id=out_init,inames=i}
             out_tmp = out_tmp + alpha[i]*a[i,j]*b1[j] {id=out_up1,dep=out_init}
@@ -385,7 +385,7 @@ def test_precompute_nested_subst(ctx_factory):
     ctx = ctx_factory()
 
     knl = lp.make_kernel(
-        "{[i,j]: 0<=i<n and 0<=j<5}",
+        "{[i]: 0<=i<n}",
         """
         E:=a[i]
         D:=E*E
@@ -396,7 +396,6 @@ def test_precompute_nested_subst(ctx_factory):
 
     ref_knl = knl
 
-    knl = lp.tag_inames(knl, dict(j="g.1"))
     knl = lp.split_iname(knl, "i", 128, outer_tag="g.0", inner_tag="l.0")
 
     from loopy.symbolic import get_dependencies