diff --git a/tests/core/test_em_asm_2.cpp b/tests/core/test_em_asm_2.cpp
index 91e40e3911000..92721ad11eaa7 100644
--- a/tests/core/test_em_asm_2.cpp
+++ b/tests/core/test_em_asm_2.cpp
@@ -102,11 +102,11 @@ int main()
   i = EM_ASM_INT("{console.log('5. got int ' + $0); return 7.5;}", 42); printf("5. returned int %d\n", i);
 
   printf("\nEM_ASM_INT: Return an integer in a single brief statement.\n");
-  i = EM_ASM_INT(return HEAP8.length); printf("1. returned statement %d\n", i);
-  i = EM_ASM_INT("return HEAP8.length+1"); printf("2. returned statement %d\n", i);
-  i = EM_ASM_INT({"return HEAP8.length+2"}); printf("3. returned statement %d\n", i);
-  i = EM_ASM_INT({return HEAP8.length+3}); printf("4. returned statement %d\n", i);
-  i = EM_ASM_INT("return HEAP8.length+4"); printf("5. returned statement %d\n", i);
+  i = EM_ASM_INT(return 42); printf("1. returned statement %d\n", i);
+  i = EM_ASM_INT("return 42+1"); printf("2. returned statement %d\n", i);
+  i = EM_ASM_INT({"return 42+2"}); printf("3. returned statement %d\n", i);
+  i = EM_ASM_INT({return 42+3}); printf("4. returned statement %d\n", i);
+  i = EM_ASM_INT("return 42+4"); printf("5. returned statement %d\n", i);
 
   // Note that expressions do not evaluate to return values, but the "return" keyword is needed. That is, the following line would return undefined and store i <- 0.
   // i = EM_ASM_INT(HEAP8.length); printf("returned statement %d\n", i);
diff --git a/tests/core/test_em_asm_2.out b/tests/core/test_em_asm_2.out
index 10ca9d7d5a252..9ee29c6c2c286 100644
--- a/tests/core/test_em_asm_2.out
+++ b/tests/core/test_em_asm_2.out
@@ -113,11 +113,11 @@ EM_ASM_INT: Return an integer back.
 5. returned int 7
 
 EM_ASM_INT: Return an integer in a single brief statement.
-1. returned statement 16777216
-2. returned statement 16777217
-3. returned statement 16777218
-4. returned statement 16777219
-5. returned statement 16777220
+1. returned statement 42
+2. returned statement 43
+3. returned statement 44
+4. returned statement 45
+5. returned statement 46
 
 EM_ASM_DOUBLE: Pass no parameters, return a double.
 1. returning double
diff --git a/tests/core/test_emptyclass.cpp b/tests/core/test_emptyclass.cpp
index 09327f9a88418..8f9d88bee315a 100644
--- a/tests/core/test_emptyclass.cpp
+++ b/tests/core/test_emptyclass.cpp
@@ -12,7 +12,6 @@ struct Randomized {
 };
 
 int main(int argc, const char *argv[]) {
-  new Randomized(55);
-
+  Randomized(55);
   return 0;
 }
diff --git a/tests/test_core.py b/tests/test_core.py
index a897565d32a0f..9abf86e098451 100644
--- a/tests/test_core.py
+++ b/tests/test_core.py
@@ -274,7 +274,7 @@ class TestCoreBase(RunnerCore):
   def is_wasm2js(self):
     return self.get_setting('WASM') == 0
 
-# A simple check whether the compiler arguments cause optimization.
+  # A simple check whether the compiler arguments cause optimization.
   def is_optimizing(self):
     return '-O' in str(self.emcc_args) and '-O0' not in self.emcc_args
 
@@ -1837,8 +1837,8 @@ def test_em_asm(self):
     self.emcc_args.append('-std=gnu89')
     self.do_core_test('test_em_asm.cpp', force_c=True)
 
-  # Tests various different ways to invoke the EM_ASM(), EM_ASM_INT() and EM_ASM_DOUBLE() macros.
-  @no_asan('Cannot use ASan: test depends exactly on heap size')
+  # Tests various different ways to invoke the EM_ASM(), EM_ASM_INT()
+  # and EM_ASM_DOUBLE() macros.
   def test_em_asm_2(self):
     self.do_core_test('test_em_asm_2.cpp')
     self.emcc_args.append('-std=gnu89')
@@ -5944,6 +5944,10 @@ def test_ssse3(self):
   @is_slow_test
   def test_sse4_1(self):
     src = test_file('sse/test_sse4_1.cpp')
+    if not self.is_optimizing() and '-fsanitize=address' in self.emcc_args:
+      # ASan with -O0 fails with:
+      # Compiling function #69:"__original_main" failed: local count too large
+      self.emcc_args.append('-O1')
     self.run_process([shared.CLANG_CXX, src, '-msse4.1', '-Wno-argument-outside-range', '-o', 'test_sse4_1', '-D_CRT_SECURE_NO_WARNINGS=1'] + clang_native.get_clang_native_args(), stdout=PIPE)
     native_result = self.run_process('./test_sse4_1', stdout=PIPE).stdout
 
@@ -7577,6 +7581,7 @@ def test_asyncify_indirect_lists(self, args, should_pass):
       if should_pass:
         raise
 
+  @no_asan('asyncify stack operations confuse asan')
   def test_emscripten_scan_registers(self):
     self.set_setting('ASYNCIFY')
     self.do_core_test('test_emscripten_scan_registers.cpp')
@@ -8742,9 +8747,9 @@ def setUp(self):
 # Add DEFAULT_TO_CXX=0
 strict = make_run('strict', emcc_args=[], settings={'STRICT': 1})
 
-lsan = make_run('lsan', emcc_args=['-fsanitize=leak', '--profiling', '-O2'], settings={'ALLOW_MEMORY_GROWTH': 1})
-asan = make_run('asan', emcc_args=['-fsanitize=address', '--profiling', '-O2'], settings={'ALLOW_MEMORY_GROWTH': 1})
-asani = make_run('asani', emcc_args=['-fsanitize=address', '--profiling', '-O2', '--pre-js', os.path.join(os.path.dirname(__file__), 'asan-no-leak.js')],
+lsan = make_run('lsan', emcc_args=['-fsanitize=leak', '--profiling'], settings={'ALLOW_MEMORY_GROWTH': 1})
+asan = make_run('asan', emcc_args=['-fsanitize=address', '--profiling'], settings={'ALLOW_MEMORY_GROWTH': 1})
+asani = make_run('asani', emcc_args=['-fsanitize=address', '--profiling', '--pre-js', os.path.join(os.path.dirname(__file__), 'asan-no-leak.js')],
                  settings={'ALLOW_MEMORY_GROWTH': 1})
 
 # Experimental modes (not tested by CI)