diff --git a/tmt/utils/__init__.py b/tmt/utils/__init__.py
index 7b3e7e1b2d..6c52586128 100644
--- a/tmt/utils/__init__.py
+++ b/tmt/utils/__init__.py
@@ -122,6 +122,10 @@ def configure_constant(default: int, envvar: str) -> int:
 log = fmf.utils.Logging('tmt').logger
 
 
+#: How many leading characters to display in tracebacks with
+#: ``TMT_SHOW_TRACEBACK=2``.
+TRACEBACK_LOCALS_TRIM = 1024
+
 # Default workdir root and max
 WORKDIR_ROOT = Path('/var/tmp/tmt')  # noqa: S108 insecure usage of temporary dir
 WORKDIR_MAX = 1000
@@ -2399,7 +2403,12 @@ class TracebackVerbosity(enum.Enum):
     DEFAULT = '0'
     #: Render also call stack for exception and each of its causes.
     VERBOSE = '1'
-    #: Render also call stack and local variables for exception and each of its causes.
+    #: Render also call stack for exception and each of its causes,
+    #: plus all local variables in each frame, trimmed to first 1024
+    #: characters of their values.
+    LOCALS = '2'
+    #: Render everything that can be show: all causes, their call
+    #: stacks, all frames and all locals in their completeness.
     FULL = 'full'
 
     @classmethod
@@ -2554,11 +2563,16 @@ def render_exception_stack(
         yield f'File {Y(frame.filename)}, line {Y(str(frame.lineno))}, in {Y(frame.name)}'
         yield f'  {B(frame.line)}'
 
-        if traceback_verbosity is TracebackVerbosity.FULL and frame.locals:
+        if frame.locals:
             yield ''
 
-            for k, v in frame.locals.items():
-                yield f'  {B(k)} = {Y(v)}'
+            if traceback_verbosity is TracebackVerbosity.LOCALS:
+                for k, v in frame.locals.items():
+                    yield f'  {B(k)} = {Y(v[:TRACEBACK_LOCALS_TRIM])}'
+
+            elif traceback_verbosity is TracebackVerbosity.FULL:
+                for k, v in frame.locals.items():
+                    yield f'  {B(k)} = {Y(v)}'
 
             yield ''
 
@@ -2657,7 +2671,7 @@ def _render_exception(traceback_verbosity: TracebackVerbosity) -> Iterator[str]:
                         GeneralError(f"Cannot log error into logfile '{path}'.", causes=[exc]),
                         include_logfiles=False)
 
-            for line in _render_exception(traceback_verbosity=TracebackVerbosity.FULL):
+            for line in _render_exception(traceback_verbosity=TracebackVerbosity.LOCALS):
                 for stream in logfile_streams:
                     logger.print(line, file=stream)